Be adventurous with how you want the finger puppet to look. Use different colored felts, or maybe add things like ears or a tail. Beads or dots of fabric paint can substitute for the usual googly eyes.
Some people like a puppet with a personality. If you want yours to look mean and grumpy, try dark purple felt and use hard things like beads. If you're shooting for a happy little friend, yellow felt and googly eyes would work well.
If you are using a sewing machine, keep your fingers away from the needle. If you are just sewing by hand, don't prick yourself!
Make sure small children don't get a hold of little parts like beads or needles.