I'm going to come out to my cuz in a letter and I need advice on what I should write. I probably will explain a ton of stuff because my cuz doesn't really know what it really mean to b LGBT, but. . . do you think there's anything worth including in my letter?
You said that your cousin doesn't know what it means to be LGBT. In your coming out letter you can explain what it means to be lgbt, keep it simple and write in your letter that if s/he has any other questions there are other resources and s/he can talk to you about it. Tell him/her that it isn't a phase and you haven't chosen this. It's up to you what you want to include, it's your letter. Be prepared for awkward, or strange questions. Be ready to calmly answer these with simple short answers in your letter. Put yourself in their shoes - they may be surprised at first and not seem as supportive as they really are, just due to the shock. If they are confused as to the differences between lesbian, gay and bi, then you might get questions you weren't expecting, such as "but don't you want to get married one day?" but do take these questions seriously - they're undoubtedly heartfelt. Include answers in your letter. Remember to keep reassuring them that you're certain, that this isn't a change that you've suddenly decided to make to your life just now. You're still the same person they knew all along, just one that's being more open with them about a part of your life. When you come out to someone, you are saying to them "I trust you, so I'm going to be more honest with you. This is me." Just tell him/her that you'll always love them. Good luck.
Maybe it's a good idea to tell your cuz what it means to you and if you want to express yourself more then tell what he/she can expect from you, people tend to accept it better when they know what's going to happen.
It might be worth looking at some of these letters for inspiration: Empty Closets - Coming Out Letters