How can I hang artwork on a rented home's walls?
There are three ways:


Use adhesive tape designed for hanging pictures. This is the easiest method to install, and the easiest to remove when you move out, because all you have to do is stick tape to the wall. The downside is that the tape can only support several pounds, so it won't work for large pictures.
Use drywall anchors. These can be installed anywhere in your wall, but they can support only up to about 50 pounds of weight. That would be enough for most pictures.
Drive screws into studs on your wall and hang the frame from the screws. This method will support the most weight, but it requires you to find the studs inside your walls. Simply screwing into drywall but not into a stud will not work well.


Methods 2 and 3 would both leave small holes in your wall when you remove the drywall anchors or screws.