One of the simplest ways to decorate after you've moved into a new place, particularly an apartment where you might not be able to do any serious repainting or remodeling is to use washi tape.
You can take a solid color and create geometric shapes on the wall, or make the outline of a city skyline. Or you can create washi tape silhouettes to frame and hang.
You can take clothespins, put washi tape on the edges, and then hang using a piece of twine hang pictures across from one side of the room to the other. Similarly, you could use binder clips instead of clothespins.
If you're looking for a personal touch, you can always grab a cardboard letter (usually sold at your local craft store), and grab a couple rolls of washi tape. Wrap the washi tape around the letter either straight across or angled. If you angle it, it will take a little more finesse and planning to get everything to line up lay smoothly.
Buzzfeed has compiled a wonderful list of ways to use washi tape to decorate pretty much anything you can think of in and around the house.
I've found that Tapeworks and Scotch washi tapes work really well and don't peel back after they've been applied. Scotch washi tape can be found pretty much anywhere, Meijer, Joann Fabrics, and, oddly enough, Staples. Joann Fabrics also has several different brands of washi tape, including some really great Disney ones or ones for children if you're looking to decorate a playroom or a bedroom.