1) Identify WHO YOU ARE.
The RPA need to know what your character's name is if they're going to ask you questions about your application, or alert you to the results of the voting! Make sure your current character's name is in the SUBJECT and in the BODY of the email you send, so that they know who you are and how to get in touch with you. :)
Don't have a character yet? Stop now. Really. If you've never gone IC and played the game, how in the world do you know you're going to LIKE it? How is the RPA supposed to know that you're going to stick around if you're given whatever you're applying for? The best thing you can do is go register a character, go IC, play for a few weeks, and get a feel for the MUSH before requesting anything special (be it a business, a jedi slot, a feature character, etc).
2) Be CLEAR and CONCISE.
State near the top exactly what you're seeking approval for, in a clear and outlined manner. Then, in an organized way, go into as much detail as is necessary to explain yourself. Try to stay on topic, and only write what really needs to be said; if you write too little, people won't have all of the information necessary to make a decision, but if you write too much, you'll over-kill the application.
It is also of grave importance that what you write actually pertains to what you're applying for. If you write a Force application that says nothing about the Force, or a business application that doesn't talk at all about the business, you've got very little chance of success because you aren't telling people what they need to know.
Last but not least- please don't combine many applications into one. If you want to apply for a Force slot, don't combine that application with a separate TP proposal or a Feature Character application. Don't apply for a business and at the same time, request something outside of the business app all in the same email. The more you clump together in one application, the longer it's going to take for the RPA to sort it out into all of the different pieces and vote on them individually.
3) Check your SPELLING.
An application full of spelling errors looks like an application that someone didn't spend a lot of time on, and it can detract from what you're applying for if it leads to a comprehension problem. Take the time to proofread your application and be sure that it's grammatically correct, with all of the right spelling and punctuation. Don't start out at a disadvantage, when you can avoid it with that one simple step.
4) DOUBLE CHECK your content.
If you apply for something that's been posted, make sure before you send in your application that you've dealt with all of the issues the post requested. If something specific has been asked for, chances are, it's IMPORTANT, and by leaving it out carelessly, you put yourself at a distinct disadvantage against a field of applicants who have answered all the questions asked of them.
You might want to take the time here to send your application to a friend or two, have them look over your content, spelling, grammar and punctuation.. they may see something you missed.
4) Be TIMELY.
If a deadline has been posted, plan to finish it DAYS in advance so you have plenty of time to proofread, run it past friends, and turn it in before the apps are closed. If you put off writing or turning your application until the last minute, and something happens IRL you weren't counting on, don't expect the RPA to understand and let you turn it in late! Deadlines are usually at least two weeks in length, and there's a whole field of applicants who had the forethought to do their apps before the last minute and make sure they were turned in. If you procrastinated, that's nobody's fault but your own. Plan ahead, and you won't get stuck. :)
5) Send it in the right FORMAT.
A mailing list will take your one email and send it out to dozens of people, who then have to access it, read it, and then vote on it. These people have a variety of different operating systems, word processing software, email clients, and other important things that effect YOUR application in ways you may not realize. Please send all applications in plain text (.txt) format, either inline (preferred) or as a .txt attachment. Make sure that you've got it properly wordwrapped, and with a decent margin, so that someone who wants to read it in their email client or print it out doesn't have to jump through hoops to make it work. Be sure you don't use any odd formatting, either, because it's likely to come out as jumbled garbage to a word processing client that can't read it properly.
5) Confirm that it GOT THERE.
The internet is a fickle thing. Sometimes, email doesn't work, either on your end, or on the end attached to the mailing list. You'll want to page or @mail the RPA Wizard between 12 and 24 hours after sending your application to make sure that it got there and in a legible format. You'll also want to keep on hand a SAVED COPY of the app from the 'sent mail' folder of your email program, just in case the deadline passes and you realize afterwards your email never got there. In instances like this, the RPA will ask you to forward your copy of the email you sent, so they can confirm the timestamp and accept it as 'on time'.
6) Worst case scenario: Take rejection GRACEFULLY.
So you gave it your best, but you didn't succeed. Be a good loser. Especially in circumstances regarding Force Users or Feature Characters, there are usually an inordinate number of applicants, and more than half of them are excellent beyond reproach. If you don't happen to make it this time, leave the RPA with the impression that you're mature enough to handle rejection and move on with life. It's natural to be disappointed, especially when you've put a lot of work into an application, but throwing tantrums only makes you look like you can't handle losing, and that's a bad quality to possess if you're trying to win a force or feature character, who by definition have to deal with losing on a daily basis as part of their job. Just think.. the next time you apply, how do you want the RPA to remember you? Behave accordingly. The impression you leave will go a long way, for better or for worse.
See also: Force App FAQ and Feature App FAQ