Look at the puppet to determine what type of voice it should have based on its "personality." Decide what the character's dominant mood will be-nice, grumpy, happy, excitable or adorable.
Consider the age of your primary audience. If you're working with children, you may want to create a more upbeat, whimsical character. If you're performing in front of adults, your puppet can be gruff, cynical or even risqué.
Give your character an interesting vocal trait like a quirky accent. Be sure it's easily understandable, however. An unusual voice is useless if the audience can't decipher what your puppet is saying. Also avoid stereotypical accents that your audience may consider offensive.
Develop a voice that comes easily to you. Be sure you can vary the tone to reflect different emotions, shout in a large theater, laugh, whisper or even sing. If you have to strain your voice to maintain the character's intonation, you'll have trouble maintaining it and could possibly hurt your vocal cords.
Practice the voice so it comes naturally. Puppeteers need to be able to slip in and out of the puppet voice instantly while ad-libbing or answering questions.