A lot of thought and advice goes into how to introduce new PCs for GMs. This is understandable, depending on the game and group you need a way to integrate the new PC that feels natural to the story and works within the confines of your plot and events that are going on. At least if you're doing a story heavy game. Sometimes the group of adventurers just runs into the last surviving member of another party that just happened to be a room ahead of them in the dungeon - even though nothing behind that other party ever showed or helped the PCs.
The thing is though, as the player of the new PC you also have a responsibility to make it go as smooth as possible. Here are a couple of the things you should be looking for as the Player.
You Have A Greater Responsibility To Make Someone Who Will Work With The Party
When a game begins everyone kind of gets thrown together by fate and falls into place that way, or things were arranged for the group to know each other from the get go. Either way, a group of new PCs starting all at once begin with the understanding they need to form a group and then have their initial development. When a PC comes in later in the game that same openness may not be present. This means you have more responsibility to make someone who the group will be willing to accept and group with.
Unless you know your group really well, or your GM is really helping you out with plot significance, this means that solo acts and edgelords may not be as palatable to joining a game in progress. After all, why would an established group want someone who is an abrasive asshole, or always being dark and edgy while wandering off to cause problems into their established group?
This doesn't mean you can't reach on a new character, just that you have more responsibility for making someone that is a good fit for the group than you may have when the game first began.
You Need A Reason To Travel With The Group
The classic "you meet someone stranded in the dungeon" solved this for a lot of PCs in my old D&D days. After all, you have a better chance of surviving getting out of the dungeon with a group than solo. However, in other games it gets more complex. Your GM can help you with initial plot reasons to be with the group, but beyond that your PC needs a reason to travel with the group. This is somewhat the inverse of the above rule. Your PC needs to want to travel with the other PCs, meaning they also have to be the type of person who likes - or can at least tolerate - the type of people the established PCs are. You also need a goal that gives you reason to join the group.
You Need A Reason To STAY With The Group
Shows, comics, and book series are full of guest appearances where someone shows up, does an adventure, and then leaves. This can happen to a new PC easily too. It happens when the PC's reason to join the group is linked to the adventure the PCs are in. Once that is done, there is no longer a reason for the groups to stick together and it can feel weird and awkward.
Your GM can help with this, linking your personal need to the overarching plot, but that requires there to be an overarching plot which isn't always the case.
Which means, ultimately, it falls on you to have a reason to not only join the other PCs but stay with them. Some form of long term goal, or re-occurring objective best satisfied by being with the PCs.
This can be a continuance of the reason you joined, but generally the reason we join a group is practical in nature, while the reason we stay with a group is more emotional. So try and keep that in mind. It doesn't have to be true, but at the end of the day this PC is tying their life to a group of people who regularly get into interesting and dangerous if not life threatening situations. Why are they doing that?
Don't Give Them A Reason To Kick You Out
Finally, beyond joining, your new PC should not be rife with reasons to be kicked out of the group upon joining. I've seen this happen more than once with Rogue/Thief type characters who joined up, and then started going through the other players stuff. Yeah, yeah, it is what your character would do. That's fine. But why would my character let someone stealing from them stay in the group? For that matter, why would my character respond to that in any way but how they respond to all the NPCs trying that? Which, if you weren't paying attention, is to hit the thing with a sword until my stuff, their stuff, and XP falls out.
The point being, the first few days/weeks/sessions of traveling together is very much a feel out period. No relationships are particularly strong. Other players will give new PCs the benefit of the doubt often - they know you're trying to get into the game - but especially in heavy roleplay groups, that still means they're feeling out your character. So try not to be a jerk. And if you are a jerk in character, be the kind of jerk that is not a jerk to the other PCs and that does their jerkiness in a likeable way.