There are many different ways to make mortises, but likely the most common is with a router. This video shows the process with everything explained.
Again, this morning I was checking out YouTube videos about my favorite things in life, one of which is woodworking. I found this video from Marc Spagnuolo (a.k.a. The Wood Whisperer) about how to make mortises with a router. I've seen a lot of videos on this, and even have a few previous posts about them. However, if you are new to this kind of technique I thought this particular video would be super helpful.
He explains what kind of bit he uses and why. He clearly show simple layout on the first piece and then layout transfer for precision on identical pieces. One thing I noticed is that he uses a router guide, which I personally don't have. While this is probably the easiest way to do it, if for whatever reason you don't have a guide then just build one with a straight edge.