The approval process in my case was instantaneous, but I've heard of people facing problems with Adsense approval.
First thing first, if you have an existing account it takes no time. You just click the link in your earnings settings and that's about it.
The process with a new account is somewhat different. For the most part, I believe Google takes a look at your Google account, and sites you submit.
Older Google accounts have been known to get approved faster (which was the case with my account too).
All the best, and high earnings to you!