First off use a pen preferably blue or black. Take a little white out with you. You'd be surprised, how often you need it.
Take a cheat sheet with you, always. Past jobs(names, address phone numbers and bosses)Keep a list of references with name, address if possible, phone and/or email. This will help you measurably when filling out the application. come on, face it....it just looks bad to have to excuse yourself and borrow a phone book. Even if it's an online application, keep the cheat sheet, it's easier.
Next: Take the time to fill out every blank. Many times this is a test. If it's a 10 page application, fill all of it out. Believe me, I've had my share of those. the point is, this is a test. If you don't fill out every last blank, every last page it's a sign you must not want the job very much.
Go back over every answer after you're done. Make sure everything is just how you want it. Attach your resume and hand it in, or send it.
Never ever assume, just because you gave them a resume you won't have to fill out the application. It doesn't work that way, you still have to do that to. NOW, if you are doing this in person, ask to speak to the manager, hand him the application and ask him if he can give you an interview. If he can't right then, before you leave, make an appointment for one. If it's email, or he just doesn't want to be pinned down, call within 3 -4 days. If for some reason you don't get hired...hey, it happens, stop in about once a month and just check and see if they need anyone yet. Many times, they hired the wrong person. Just keep checking back, the next time they need someone, odds are they'll think of you first. go in person if possible, but at least call. Calling is better then email, it's more personal, and going is better then calls.