According to Succeedsocially.com's outstanding article these are some steps you can take: (click the link for their full article)
Steps to joining a group
Depending on your particular situation and the group you want to join, not every step may apply.
When some people talk of not knowing how to join a group, this is where they're stuck. They've got a group in mind they want to join, but don't know how to begin talking to them. Your options for making the initial contact mainly depends on the access you have to the group. Here are the two main possibilities:
Introduce yourself to everyone at once
You work at a big company. In the cafeteria you notice there's a group of co-workers from another department who seem right up your alley. One day you ask if you can sit with them.
You live in a dorm, but haven't clicked with anyone on your floor. However, you know there's a fun-seeming social circle a floor below. One Friday night you pop down, see everyone hanging out in the lounge, where you figured they'd be, and ask if you can join them.
There's a gaming store on your campus, and every time you've walked by you could see a bunch of regulars hanging out and playing Magic: The Gathering. You walk in one day, introduce yourself, and explain how you're a fan of the game and looking for a group to play with.
I realize it takes a certain amount of guts to go up to a group of people and insert yourself into their conversation. You may worry it comes off as desperate. But if you're their type, and you generally come off as likable and confident, it can all go quite smoothly. If that makes you too nervous, you could always try the next option.
Here I'm talking about cases where you still have to go out of your way to make contact with the group, and don't have an in through a mutual friend or something like that. There are many ways to go about this, but here are a few examples. Again, this is just another option for meeting the group's members. It shouldn't be thought of as a way to subtly worm your way into a clique that would reject you if you approached them more directly:
You've noticed a group you want to join that's in two of your university classes. In a third class it's just you and one of the members. You get to know her in that class, and once you're friendly with her, start sitting with the whole group in the other two courses.
You play in a rec volleyball league and have noticed one of the other teams is a group of buddies who seem fun. A few weeks later at a league-wide end-of-season party you start talking to one of the guys and seem to get along. You ask him to introduce you to his teammates, which he does.
You work as a busser in a fairly big restaurant and want to get to know the bartenders, who you don't get much of a chance to talk to during your shifts. You become friendly with one of the servers who hangs out with them. When they go out after work one day she invites you along.
There's a group you've seen around campus that you're interested in, but aren't in a huge rush to become a part of. You know some members will be at a party you're going to. You make a point to strike up a conversation with them there and hit it off fairly well. Over the next few weeks you chat to them briefly when you cross paths. About a month later you see them out at a bar with the whole group, say hello, and get to meet everyone else.
However you first make contact with a group, if you're a good fit for it this step may be the only point of struggle, and once you've broken the ice the rest will take care of itself.
Find a way to hang out with the group consistently and become closer with everyone
Assuming you didn't effortlessly become accepted and ingrained in the gang as soon as you meet everybody, the work will be in moving from 'The group now knows I exist and seems okay with me' to 'I spend time with them regularly and consider them friends'. The next few sub-sections will cover parts of this process.
Figure out how to get in on the group's get togethers
A barrier some people run into it they'll successfully make initial contact with a group and become friendly with it in a light, casual way. However, they're not getting in on the fun group activities that were one of the reasons they wanted to join it in the first place. Like they may now be able to chat to a group of guys in one of their classes, but not hang out with them on the weekends.
If you're in this situation there are a few things you can try:
Like with making friends in general, you may just need to get it on the group's radar that you're someone they could hang out with outside of the context they first met you in. Once you let them know that you enjoy the same activities they do, they may get the picture and start keeping you in the loop (e.g., "You guys play poker every Thursday? I've been playing the last few years. I'd be down to join your game if you have room.")
You could ask about future plans, and then politely ask if you can get in on the action.
You could try arranging a get together yourself. Even if everyone can't make it, it will still send the message that you're interested in hanging out with them. For this suggestion you've got to use your judgment about whether it would be appropriate. Some groups are fine with newer members trying to make plans. Others are more established and set in their ways, and will tune out ideas that don't come from their long-time friends.
If you got into the group through one or two people, get connected to the other members
This point applies whether you met the whole group from scratch, or were introduced to them through your best friend. Another group-joining problem people have is they'll start hanging out with a group regularly, but don't feel like they're a real part of it. Even if everyone is nice to them, it's still more like they're perpetual guests of the friend(s) who got them into the group to begin with. Aside from just putting in more time (see below), here are some ways to help dig yourself out of that situation:
Of course, when you're all hanging out together take time to break away from your original friend(s) and get to know the other members. Make it implicitly clear you want to become closer with everyone, and not just accompany your buddy to the odd get together.
Get the other group member's phone numbers and add them on whatever social networks you all use. Aside from allowing you to get in touch with them, and sending another message that you want to get to know the whole group, it also frees you from having to rely on your closer friend(s) as your sole avenue for hearing about their plans.
Try to hang out with them regularly, and not just make the occasional appearance when your friend invites you along.
Try proposing and organizing a plan of your own, if you think that would fly with the group. Again, it signals you want to hang out with the group as a whole and subtly implies you're an insider who's trying to arrange a get together with his or her fellow members.
You don't have to become equally close to everyone, or have them all like you to the same degree
While you want to get away from just being seen as the guest of one or two members, it's okay if you don't become super best friends with every last member. In most social circles not every relationship between the members is equally close. Sometimes two members may not even like each other that much, but they maintain harmony by keeping it to themselves and staying out of each other's way when everyone hangs out together. As long as a group on the whole wants you around, it's okay if you don't have a super strong connection with a few of the people in it. Most groups aren't like a stereotypical high school clique where a Queen Bee single-handedly rules on who's allowed in, or the existing members only accept new ones after a vote.
Once you're hanging out with the group consistently becoming more enmeshed in it is mostly a matter of time. If you put in enough hours with them they'll naturally start to think of you as a member. You'll get to know everyone better, even if it's only a light 'activity buddies' group. You'll get in on their private jokes and be part of the new ones that develop. You'll go through shared experiences. Mostly this will happen automatically, but you can speed the process along somewhat by consciously adapting and applying the ideas in this article on growing relationships.
Sometimes when you join a group you'll feel like a full-on member right away. Alternatively, you might feel like a hanger on for a few months. That doesn't necessarily mean the group doesn't like you, just that if some members have known each other a while it's inevitable that they'll be more drawn towards each other, and might unintentionally leave you out somewhat. Once you're hanging out with the group on a regular basis, you're in. Don't look that gift horse in the mouth. Just keep showing up and doing what you're doing and over time you'll hopefully get to know everyone better and become more of a core member.
Accept that once you've gotten your foot in the door with a group, it still doesn't always work out
Exposure and familiarity generally increases bonds between people, but it's not guaranteed. Sometimes you'll join a group, feel on thin ice the whole time, and then eventually leave when you realize you'll never be fully included. This article, and the ones it links to, cover that issue in more detail. It's an uncertain, risky period you need to be willing to go through. Hopefully any feelings of being a second-tier member are only temporary. If you really feel yourself struggling it may be a sign the group isn't a good match for you. Often when it works out it feels quite easy from the get go.
Some overall thoughts on joining groups
I just gave a rough set of steps for joining a pre-existing group. Here are some general thoughts on the process:
I already got at this idea a few times already, but I'll repeat it. The idea of joining an established group can seem more daunting than it often is. As I mentioned at the start of the article under some circumstances you really don't have to do much to get in with one. Often this is the case when you're new on a scene somewhere. It's not unusual for a new person to quickly get pulled into an existing group. If it doesn't happen automatically, it's still often quick and easy to execute purposely. For example, if you've started an internship at a new company and there's a group of eight employees who all hang out and are similar to you, joining their group may take nothing more than asking if you can join them on break, and if all goes well, acting from then on as if you're part of the pack.
People are often more nervous about trying to join an existing social circle when they and the group have been in the same environment for a while. You may worry about how it will come across when you suddenly want to join a group you haven't shown an interest in until now. However, if the group is friendly, compatible, and open to new members, they may be quite welcoming. They may even be glad you've finally decided to start hanging out with them, and were wondering what took you so long. That or they never gave you much thought until now, so they don't see you suddenly wanting to join as weird or out of place.
Don't put the group on a pedestal
It's fine if you want to join a group, but try not to psyche yourself out too much by seeing them as this awe-inspiring, imposing collection of people who you'd do anything to be accepted by. Even if you don't see them as that impressive, just the fact that trying to join a group can be nerve-racking for some people can imbue them with that aura. They're just a social circle. If you don't get in with them it may be disappointing, but your life won't end. There are always other opportunities to make friends.