You pretty much download the ISO images, burn them to a CDROM (not copy the image to the cdrom, but burn it TO the cdrom...)
After that is done, you pop in the install disk and follow the directions. If you don't know what to do then just accept the defaults. They are usually the safest selections.
Pick "install everything" if you can (modern linux distro with everything can run 4 gigs of harddrive space) any services and such you don't want running you can always disable them at a later date, or uninstall them.
The major snags that happen is usually hardware related, caused by lack of proper support by hardware companies. Two major things to watch out for is if your using a Nforce (1 or 2) board the onboard ethernet probably won't work without propriatory drivers from nvidia.com, ATI video cards newer then 9200 (I think) can cause issues. Usually you pick the "VESA" driver if the default doesn't work (but try the defualt or ATI or nv for nvidia drivers first, they give good performance), vesa is a minimal compatability standard for video cards and almost all modern cards are compatable. Laptops can be difficult, as also lots of wireless lan cards.