A decade ago I made these finger puppets out of felt for my first child to entertain him in church. Although they are a little worse for wear, they have helped us get through many church meetings and have been used by all of my kids. They are so simple to make.
I just bought a variety of colors of pre-cut felt squares (from JoAnn’s I believe). Then I looked at pictures of cartoon animals to give me some ideas of how to shape the individual animals faces. I cut out 2 upside-down U shapes and used my finger to measure. I made sure I left enough room to glue the two pieces together with my glue gun and still ensure that my finger would fit into the hole. I added a pair of google eyes to each puppet. These would also be fun to make and give as a gift to a new mom or a one year old celebrating her/his first birthday. Or you can make them together for your own kids.