First, read everything on this site:
http://www.leaseguide.com/
Everything.
Then, download a lease spreadsheet and start playing around with it to see what your monthly payment will be. We can answer specific questions you may have.
Re: negotiations, it's pretty simple. After you've decided the car you want, go to a dealer that minimizes your MF (ideally the base rate) and your selling price so that you have the lowest monthly payment. Residuals cannot be altered.
If you want us to look at a sample case, please give us: type of car, # of months, # of miles/year, MSRP with options and destination, selling price with options and destination, State, and tax rate.