I know that most parents are not up for a mess all the time (or ever!). Cutting, manipulating and gluing paper is a great way to have a meaningful art experience without much mess.
Some little ones will just want to cut or just want to fold and may not wish to "make" something at all. That is OK. Resist the urge to guide too far. If your child is happily cutting and does not wish to glue, allow them the freedom to do just that. Try not to teach too much. Young artists do not need their work to look like something. Help only when asked.
I gave Hollin a sheet of red 12" x 12"cardstock for the base. The size and color do not matter, but it should be sturdy. Then, I grabbed some scraps from our scrap bin--repurposed art projects, cut-up greeting cards, scraps of construction paper etc. I did control this a bit by selecting fairly sturdy pieces and cutting them into long strips and basic shapes. I showed her how to wrap a strip around a pencil to make a swirl and how to fold a strip back and forth to create a zig-zag. I made a few other folds and cuts on my own then left her with the glue and scissors and with a sheet of round stickers. She got really into this. She created a playground with slides and stepping stones and all sorts of interesting playthings. At one point I had to hold myself back from committing a major creativity killer. She was telling me that tiny little children would have so much fun playing on the slides and walking on the bridge. She was deep in play. I almost grabbed some little stickers of animals or people for her to use but thankfully I held back. She did not need that, she had everything she needed to create a magical playground in her head and on the table. Little images would have destroyed the aesthetic value and more importantly they would have sent the message that you need to have all the props in order to play. I hope this makes sense and that I am not sounding like a lunatic!