I have a fairly successful Youtube channel with an entirely different subject matter but here are the things I have done to promote it and I have a little over 5100 subscribers and counting.
Make sure you use good keywords such as: puppets, muppets, comedy, sketch, show, etc. Use as many as you can think of as long as they pertain to your video. Come up with a set of keywords that relate to all of your videos and keep them handy in a text document so you can just copy and paste them onto all of your videos but also do video specific keywords if your videos have different subjects.
Make sure you have a descriptive title. Avoid calling your videos "Show Name: Episode 1".
If you have a variety of different videos organize them into playlists on your Youtube channel.
At the end of your video provide a link in the video to subscribe or provide a link to your previous video or to one of your playlists. A good example of this can be found at the end of most
Glove and Boots videos.
Find other people with similar content. Do video responses to their videos. Leave comments on their videos and try to mention that you have similar content without seeming like you're spamming.
Try to do collaborative work with other people with similar content. Maybe have your puppets skype with the puppets from another channel.
Ask people with similar channels to do a promo for you and do a promo for them in return.
If you don't mind revealing "trade secrets" do a puppet making tutorial or a behind the scenes video and show people how you make your show. Some people might not want to do this because it breaks the illusion but tutorials bring lots of views.
Encourage audience involvement by having a contest or giveaway. When people comment on your videos or hit the like button it makes your videos rank higher in search results. Contests can push people to comment.
Try to come up with a catchy theme song but keep it short. 10-15 seconds max. I got a guy on
fiverr.com to do a theme song for me and people have told me they catch themselves humming it sometimes. It was well worth the $5.
Make sure you have good lighting and audio. The two biggest turn offs are bad lighting and muffled audio. Even if you have great content people will turn it off if its hard to see or hear what's going on.
Hopefully this is helpful. A lot of the stuff I do on my channel isn't relevant to puppets.