If you’re changing from a dark colour to a light colour, I would paint the room white first so that the next colour you are painting has a solid base and you should only need two coats of the new colour.
Before you start, cover your furniture and your floor. Put on some old clothes. You may be using a roller for the main job but I find I’m covered in a thin spray of paint at the end of the job without even realising.
Tackle one wall at a time. Take a brush and “cut in”—paint along the corners, edges and trims from top to bottom. When applying paint with the roller, use long strokes in a W pattern for ample coverage (and to avoid roller marks). Once the wall is dry to the touch, it’s ready for a second coat.
Depending on the job, use tape on the edges of windows, skirting, coving etc. but I tend to try and keep to a straight line with a steady hand. Totally up to you, whatever you feel comfortable and confident doing.