Well - I found two great books: "Shape By Shape" and "Shape by Shape Collection 2" by Angela Walters. Each book has more than 70 different stitching patterns, with easy-to-follow directions and lots of sample photos.
One of the things she recommends is to try drawing out the design you want with a pencil and paper (or, as I've done, with a whiteboard and marker). It helps a lot to work out the motions associated with the patterns - and I found even simple patterns can be more challenging than you expect when you start out. Much, MUCH better to make mistakes on a whiteboard.
Next I grabbed some scraps of fabric and batting and set up a small practice sandwich to mount on the longarm. And away I go!
These wavy lines were fun to do - but, as you can see, keeping the lines straight wasn't all that easy.
I had better luck with the patterns below, especially the wavy feathers on the bottom.
Here's one (below) that didn't work out quite so well. I'll have to practice that one quite a bit, I think. The sample in Angela's book looks terrific. I'm sure I can refine my technique if I keep working on it.