Comment It'll Just work..... (Score 5, Informative) 172
Set the SSID the same for each AP. Set them on different channels so that the AP's don't "step on" each other's bandwidth. Roaming is a station-side (client in common usage) decision, so your PCs will automatically pick the AP with the best signal strength.
As far as authentication goes, this all depends on the AP. All should support PSK (preshared secret keys, aka passwords) and in that scenario, set them all to the same value on each AP. The PSK should be at least 24 characters long, and the SSID for the net unique to keep the security at acceptable levels and reduce the possibility of offline dictionary attacks against the PSK.
Assuming the APs support it, Enterprise grade authentication with individual per-user passwords is within reach at little to no cost. You can tie into Active Directory or set up a free AS (Authentication Server) using FreeRadius on a linux box. The definitive reference for doing this with an MS server is a book titled "Deploying Secure 802.11 Wireless Networks with Microsoft Windows". Make sure you check for updates to the book online, and there is an appendix which details how to set it all up in a lab environment, which will let you prove principle without screwing with the production network.
Google around and you will find loads of information on how to do this with Open Source, the key articles being some from Linux Journal from about 6-8 years ago.
Hope this Helps......