Hi, Branwen. Installing a door is pretty easy but does take some tools. The first, and hardest, part is the hinges and, yes, you will have to mortise both the door and frame. Measure down from the top of other doors in your house to get the hinge location, hold the hinge in place and score around it with a utility knife. Use a chisel to mortise up to the score line. Use a Vix bit to center the holes in the hinge holes and install the screws. Work very carefully on this because you care in installing the hinges will show up immediately in how well the door works.
Installing the doorknob is a little easier because it will come with excellent directions and a template, but you will need some special drills for this. You can usually buy all the special drills all in one package at your home center.