I got my start scratchbuilding making paper models from plans I got for free on the internet. I just printed them on the appropriate card stock or paper and made them. Then I started printing them on really thin paper and transfering it onto plastic card. Then I started designing my own and making the parts I wanted. Sometimes I go back to cardstock when I need something to curve or bend.
You can get the plastic from most model railroad shops or a good hobby shop. The most common stuff available is made by Evergreen:
http://www.evergreenscalemodels.com/
Plastruct is also a good source
http://www.plastruct.com/
Also -- at home depot or a similar place, sometimes you can find flat sheets of styrene that are meant as light covers for big florescent lights. This stuff is nearly as good if you don't need a texture and quite cheap in comparison
EDIT: Added the home depot thing