You can also simply hand piece. Grandmother's Flower Garden and other hexagon-shape patterns are often easier to hand piece than to machine piece. Or, you can simply hand-piece 9-patch blocks. Hand piecing can go surprisingly quickly using Jinny Beyer's methods. Check your library for one of her DVDs or videos -- quite eye-opening!
I'm sure there are DVDs and videos available that teach needleturn applique too. Instructional DVDs can get pricey, so I would definitely check with your local library first. If they don't have something appropriate, go to their desk and ask about the possibility of inter-library loan.