Hi.
You have arrived at the documentation area for the OpenWrt project; this is the summary page I wish I had found a couple of hours ago before diving in.
1. How OpenWrt differs from other replacement firmwares
Technically, OpenWrt is designed to be customisable and modular - Lego instead of Hungry-Hungry Hippos, if you will - it's basic by default and has a package system for adding just the bits you need.
Philosophically, OpenWrt is, as the name suggests, open source - there are no commercial versions with extra features, no subscriptions, the source is available.
Practically, installation can be easy but you need to read up to make sure you are installing the right thing. I didn't, and the resulting hassle prompted me to create this page. Documentation is found in this Wiki and in some standalone web pages linked from here. Where it is sparse or missing, read and search in the forums. Support is self-help and forum based. Chat/discussion is in IRC.
2. Summary of OpenWrt software
There are two main versions:
whiterussian - Only for Broadcom hardware, more documentation and tutorials are aimed at this version. Development stopped in early 2007.
kamikaze - Supports multiple hardware architectures, uses the 2.6 kernel for all targets except a legacy Broadcom target (to keep Broadcom wireless functionality.) Uses config files to store configuration instead of nvram.
There is a project aimed more at user friendliness (OpenWrt plus an updated web interface) http://x-wrt.org/ - You may well want this version.
3. Notes before your first install
- The IP address of a fresh install is 192.168.1.1, and it's listening for telnet connections only.
Read the forum thread common mistakes. It explains the two types of firmware file, the steps the routers take when booting up and several other bits of useful information.
Your next step is probably the Install Guide. Enjoy, and don't panic.