spazdaq:
write your own letters of recommendation.
then ask the person to sign it.
I vote that this is the worst idea of all time (for like the last 5 minutes).
EDIT: I have known at least one professor who asked a student to write the letter himself, but it was only after the student asked the professor to write one for him, and it was because the professor had been working very closely with the student for 3 years and they were on a quite chummy, beer drinking basis, so he knew the kid wouldn't be stupid about the letter. But going in and asking them to sign something you wrote is a quick way to get sent out of the office without much of a second chance. ENDEDIT.
This is something that works when going from high school to undergrad because undergrad is easy and nobody gives a shit.
Graduate school is entirely different and you're actually supposed to make a career out of this, so in my experience, letter writers take it much more seriously.
Everything I write here is specific to my experience in physics, but I assume that neurobiology is similar in acceptance difficulty, so it shouldn't be off the mark too much.
First, think back about any professor upon whom you made an impression. Did you get a good grade in his class recently? Does he remember you? Did you do research for him? If the answer to all these questions is no, then you're dumb. Why didn't you make better use of your time in undergrad?
Nevertheless, look next to any relevant research you've done outside of undergrad. You worked for some labs, right? Talk to your supervisors and ask them if they'd be willing to write you a good letter of recommendation.
It's important that you know they will write you a good letter. There was a story of a guy who basically putzed around in undergrad and, in a panic, needed some letters of rec. So he asked one professor from whom he had a class to write him one. The professor admitted that he had never seen the kid before because the class was a while ago and the student never went to office hours or talked to the professor, so he wouldn't be able to write anything positive about the student. But the guy was desperate and asked if he'd write one anyway, and after a few requests, the professor said he'd write him a letter. The professor turned in a rather scathing letter that basically detailed the story with the student and said that he never made an effort to get to know the professor and only scored average in the class. Needless to say, the kid got rejected everywhere.
So don't be that guy. Get to know people first. Your letters figuratively can make or break your application. I wouldn't have been accepted where I was without such outstanding letters, and that's because I put in the effort to do research and contact professors while in class.
I say that because if you DON'T know anyone, you'll save yourself hundreds of dollars in application, GRE, and transcript fees by just waiting another year and continuing with research. Some institutions even have spring admission if you don't want to wait that long, but it's probably some no-brain PhD like History or English Literature.
Beyond this advice, the impossibly attractive Virginia is absolutely right. Ask in person, and make it very clear what the deadline is. Professors have shit to do, and if you don't gently remind them now and again after they agree to turn in their materials, they'll forget. If the deadline is in two weeks, you've blown it so don't even ask because they'll just get pissed off at you anyway. Explain also the type of program you're applying to and the institutions at which you hope to gain acceptance. This may go some amount if the professors recognize the prestige of particular places and so they may tailor the letter accordingly. Probably not, however. Explain why you want to go to grad school and why you want them to be the one to recommend you.
I know of no formal way of asking other than that in your application materials for your school, you'll be given either an electronic section to fill out with the email addresses of the professors, or a printout sheet that you'll have to physically give to the professors (along with envelopes and stamps!). This, of course, should be done well AFTER you have the in-person talk about the recommendation.
