Before you start looking, decide what features you need and what you're using the laptop for - same as if you were buying a new desktop PC (only probably more expensive). How big a hard drive, how much memory, do you want to watch DVDs, do you want to burn CDs, do you want to burn DVDs? Do you need wireless internet? What kind of software will you be putting on - or is the basic Microsoft Works package fine for your needs? Do you want Windows or a Mac?
Then, check "slick deals", Dell, and your local computer sources - Circuit City,
Best Buy, CompUsa, Office Max, Staples, Office Depot, Apple Store, etc. Go in and try a few out - is the screen bright enough, how are the keys to touch, listen to a CD, etc. Plan to spend at least an hour and a half or more - probably just browsing. Tell the guys who hover around you that you are looking, and what your usage intentions are. Hopefully, you'll get someone willing to help out - especially if they think you will come back to them later.
Get the model numbers of the one(s) you like best. Go to "cnet" and look for reviews. Go to the manufacturer's website and check their support section - are there lots of support bulletin updates or just a few? What is their repair history, what are they rated, etc. ?
Are you willing to consider an "open box" or "refurb"? These can save you big bucks on higher-end machines. Look up the prices at the store and online. Back-to-school time can be a good time to find a bargain, but then again so can Black Friday, or even just after Labor Day. And if you live in or near Delaware, you'll save all that sales tax!
Good luck!