In my experience, there are a few things to remember.
1. Show interest in the game. Not a game, but THE game. I recently finished advertising for a game and making selections. One person had a very long and detailed application. The application got thrown out at the same time as the incomplete applications. Why? The application was very clearly a copy-paste from another, very different game. I think one word got changed from the original to give it even the vaguest of ties to the world I was using (which has tons of lore that anyone can read). Avoid this in your own search for a game. If the DM gives lore for the world, search for a way to incorporate some of it into your background. If the description of the game says that arcane casters are mistrusted, feared, and hunted, then if you apply with a wizard, you had best make sure the background has him avoiding detection or dealing with "authorities".
2. Have a firm concept. Make sure your character feels like a character. The mechanics are there to back up your concept, not define it. Worry about your concept first, then pick the mechanics to fit. Don't be afraid to ask for help (there are a lot of folks on these boards that would be happy to do so), just make sure you post what your concept is and all relevant rules (including allowed sources and houserules) and your own preferences. Be ready to stick to your guns on your concept, but also ask the prospective DM about it. If he says your concept won't work in the game, it's best to change your concept. Just be sure it's the concept and not mechanics he doesn't like.
3. Meet all the requirements. This sounds stupid, but I'm serious. Incomplete applications don't get considered to be players. The DM went through the time setting up the game, lore, houserules, and looking at applications. You should put in the time to at the very least deliver a completed application. These requirements change from DM to DM and game to game. Be sure you have the right set of requirements.
4.Learn from your failures. I was lucky and got into the first game I ever applied for on myth-weavers. I am also a tiny minority in that. If you are rejected, analyze your application from the viewpoint of a stranger and ask yourself the question "would I have accepted this application?" This is difficult as you need to really remove yourself as the writer of the application. If you're not sure why you were rejected, send a note to the DM asking why you didn't make the cut. Most will respond with helpful advice to improve your application.