Just to add to what's been said: if you've been a Windows user until now, you're probably used to visiting sites that offer Windows software, so you'll have to go find the sites now that host Mac software — and trust me, there's some terrific stuff.
A good place to find nearly any kind of program is Versiontracker.com, but if you want recommendations, read some of the application suggestion threads in this very forum. 95% of Mac software will be downloaded as a disk image (.dmg) file, with a small amount compressed as a .zip or .sit file. Installation is almost always simply mounting the disk image and dragging the application icon to your own Applications folder.