You gotta start somewhere, don't you? As a starting project I chose the shopping bag tutorial by Anna at the Pleasant View Schoolhouse (http://pleasantviewschoolhouse.blogspot.com/2007/11/how-to-sew-cloth-shopping-bag.html).
A great tutorial, by the way, with lots of very nice pictures and thorough instructions.

I used some scraps of fabric donated to me by friends & family.

The proud result (keep in mind - it was my first project... ;-) ):





































Edit: In the meantime I have already finished two more of these shopping bags, using one of Ikea's sturdy and cheap fabrics (trust me, the expensive stuff can wait until I really master my machine..). Sadly I've got no photos as I gave those bags away as gifts. Oh, and one of them even had a zippered inner bag. =)
I made that one following this tutorial at U-handblog (great site!):
http://u-handbag.typepad.com/uhandblog/2007/02/zippered_inner_.html
Another really good tutorial.

This is their result: