The first step towards getting an application character is to figure out what to apply for. This may seem like a no-brainer, but there's perhaps a bit more involved here than one might think at first glance, especially if you want your application to be successful.
The first thing of course is to figure out what you want in a character. This may consist of like: Warder, level 7 forms in every weapon, 10 in all attributes, large skill list, etc. OK...that's great. Now you have an idea of what you want, let's figure out what you're likely to get. The average player...ok basically all players aren't going to be successful in an application where they ask for the above. The Immortals simply don't want to grant people all that stuff, they'd rather that the player had to work for it a bit. If you submitted an application like that, it might get provisionally accepted, but more likely than not they wouldn't take you seriously and would tell you to take a hike.
So the second thing you need to do is figure out what you need in a character. If we take the above and pare it down, we would probably get something like this: Well a Warder is fine... but the status of Warder requires level 5 forms, not 7. Thus, we might ask for level 5 forms. We might then ask only for what we need in attributes to be able to use forms at that level (use statform to get an idea), and maybe toss a couple points in inte, perc, and prso or such. As for skills, well talk to other players, find out what skills you need to be a Warder, and give an actual list that seems appropriate. An example of a short list might be: disarm, parry, dodge, borderland combat, rescue, protect, mount, void, longbow, sneak.
At this point we have a more reasonable idea what we want to apply for...so now the third thing we should do is figure out if this type of thing is even reasonable. Does the MUD already have a whole bunch of that type of character? E.g. if there are already a whole bunch of active nobles, you're less likely to be able to successfuly apply for a noble. You're a lot more likely to get an application through if you are applying for something that the MUD either doesn't have many of, or has a need for. You should think about this before you write up your application. Is there a current need for that type of character on the MUD, or would it enhance the roleplay enviornment for the other players? If you think the answer is yes, then you might just be on to something.