Cutting in?
Maintain the angle of the brush throughout the entire brush stroke. The point is to keep the shape/footprint the bristles are making on the wall the SAME throughout the entire stroke.
Use full length strokes. Don't dab paint here and there 3 or 4 inches at a time. One brush, dipped in paint, can do 2 or 3 feet before you need to dip again. Maintain the angle for the entire 2 or 3 feet.
If you see misses or parts where you aren't completely straight, fix them after. Continue the stroke!!
If you notice the brush is leaving blank spots, but the line in the corner is still solid and looking good, continue cutting in. The section away from the very corner is easily fixed after.
Use normal lighting, so either from the window or ceiling.
After you dip the brush in paint, don't start right in the corner, it's easier to start out an inch or two and then go into the corner after you get the first globs of paint off the brush.
Cut a wide enough strip to allow for the roller afterwards. If you don't come down on the wall enough, you risk running the roller into the ceiling (done that so many times :p). 4 inches is good.
If you really suck at keeping a straight line, you can use tape. Do NOT press the tape super firmly into place, just make sure the edge is sealed. Peel the tape off immediately after you finish one section (one side of the room). If you leave the tape on while the paint dries, you're asking for trouble.
Clean up any drips/runs immediately. It's NOT easy to sand them down after it dries.
If you notice that you can see through the fresh paint to the colour underneath, that's fine. Why do you think we apply paint in multiple coats?
The darker the colour, the more coats you can expect to need. Especially with reds, yellows, purples, and blues. If it says "deep base" or "ultra deep base" on the side of the paint can, you can expect at least 2-3 coats depending on the existing colour. I had a purple wall, on brand new drywall, take 8 coats at one job.(including white primer).
Piling more paint on to try and make it look solid is a very bad idea.
If you're not following with the roller before the cutting in dries, blend the edge of the cutting in by using a mostly dry brush. If you leave a solid line, let it dry, and then roll over it afterwards, the line will show through.
Source: I'm a painter.