Quote Sillabub:
I'd suggest either applique with Heat 'n' Bond Lite or screen printing. With the Heat 'n' Bond you don't even need to do any sewing necessarily as it's double-sided adhesive, but doing a tight zigzag stitch around the edges will give the pieces a nice finish and prevent your edges from fraying. Using Heat 'n' Bond is very simple, too.
Screen printing is undoubtedly more fiddly but it does look nice. There's a tutorial on "fakie" screen printing
here. I haven't tried following that tutorial though so I can't vouch too strongly for how good it is.
Sillabub has pretty much covered the suggestions I would give. Just as a side point, Heat n' Bond is also known as bondaweb if you can't find it under the first name, eitherway it gives excellent results and is simple to use.
A third alternative to either applique or the 'fake' screen printing, if these don't suit you, is block printing. I used this for a costume which had a small, repeating pattern on the fabric. It's similar to the potato printing primary school children do, except I created the printing block out of sculpy allowing for a fine edge to the pattern.
Once baked, brush the paint on the block and then push down on the fabric. You may want to test it first on an old piece of fabric to see how much paint is required for an even covering.