How to join a private gang
First of all, you have to do some research. Look for gang creation posts in the forum or recruitment posts and other things that is related to gang/family section. Often a private gang states guidelines there. Find out what the gang is about, how they talk and what kind of people they want so you know what to roleplay. Also find out how to approach. Often you should call someone above rank 3 ingame. Use /families to see gangs and use /families [FamilyNumber] to see members and their ranks.
The first impression is very important when approaching such gang. It’s important to pick the right time of approach. If you notice someone is busy, don’t bother trying because you’ll mess up the first impression. Make sure you roleplay well, put maximum effort in your typing and English, and make things interesting. Don’t start with “Can I join?!”. First you want them to know you can type and RP well enough.
The Roleplay
Ask yourself how a person would join such gang in real. Sometimes it happens by becoming an employee in the cover-up organization of a gang, like Mafia’s security firm and Yakuza’s tea house. Sometimes it happens because one person asks another for help with something (could be from both sides). Maybe you can manage to become friends with someone in the gang who could recommend you.