Most of us quilt on our regular domestic machines.
Harriet Hargrave's book is really good for getting started. Here is a link to it on Amazon:
http://www.amazon.com/Heirloom-Machi.../dp/1571202366
The easiest way to quilt is to use a walking foot and make gently curving lines across the quilt. If you do this both ways, you get a curvy cross-hatching.
A lot of people start with stitch-in-the-ditch (SID), but I think that's actually fairly hard. You use a walking foot and try to stay either in the seam line or to one side of the seamline. Having to stay so precise makes me too anxious, so I don't do this anymore.
Free-motion machine quilting (FMQ) is what most of us aspire to. It can take some practice, but it is the most freeing. Harriet's book is all about FMQ.