A common and easy way to divide a living space is by building a stud wall aka partition wall. This is a great way of creating a playroom, washroom, extra bedroom etc. The stud wall is not loadbearing and simply made up of a timer frame with plasterboard on each side. Insulation can be added between the plasterboard for added warmth or sound insulation.
What you will need is the timber, plasterboard, plumb bob and line, nails, screws, spirit level, hammer and screwdriver.
It is an easy job for someone with a modicum of DIY experience.
The following links are guides and information that go into detail on building stud walls.