in general it's pretty similar to undergrad, at least so far as the process goes. you need to keep track of your deadlines and that's about it. Packages for incoming students usually come out around April-ish, unless you get picked for a monster merit scholarship, which might come sooner at some places because they are trying to recruit you.
i'm not sure i understand your question about being denied funding...? if you mean getting to third year and being told there's no money, well that shouldn't happen unless the scholarship fund was tied up in AIG stock (true story some places, there were some pretty sad people out there). even then, there are ALWAYS loans. Student doctors at LCME schools are some of the best credit risks out there, and regardless of your financial situation you should qualify for $40k+ in Staffords every year (unless your cost of attendance is lower than that).