Beginner: what software to combine 2 videos of a dance show
You are looking for a Non-Linear Video Editing packages or NLE.  Premiere and Final Cut Pro are two of the most popular, but they are also relatively pricy professional products.  There are also many cheaper and/or free options available such as Windows Movie Maker (Windows) or iMovie (Mac).  If you search for non-linear editing software or video editing software, you should find lots of possible options.