There's a good B&Q book that gives a guide to DIY but this wil tell you about everything, not just painting.
There's plenty of online stuff if you google something like "How to repaint a room"
Theoretically yes, you pour paint into the tray and get painting. That's about it.
I use a roller with a brush to do the edges and I do the edges first and then fill in with the roller. A couple of thinner coats is better than putting on one blobby thick coat.
You can get pads instead of rollers that my Wife prefers to use, but I find they don't give as even a finish as a decent roller.
Do you need dust sheets.....what are the floors like? Presumably not bare floorboards you are putting a new carpet on? So, I would get some dust sheets or cheaper plastic sheeting from B&Q or somewhere. Easier to prevent getting paint everywhere than clean it off carpet!
Do you need to masking tape the edges? Depends. It is harder than it looks to get a nice even edge, but if you are just painting white against white then it might not matter. Do you have a steady hand and be able to take your time or are you trying to get it done quick. Masking tape is an easy way to get a neat edge, but you still need to be careful as it can pull off the paint underneath. Frog tape works very well, but then cheap masking tape is also pretty good. Avoid the blue Diall stuff from B&Q. It is far too sticky.
How fresh is the paint on the walls? If it's been on there a while, you should probably wash the walls first with a sugar soap solution, but from the sounds of it, this will take all the existing paint off. But, it will remove any dirt/grease and help the new paint stick to the surface better.