Do all your prep first.
Wash down the walls and woodwork.
Fill gaps with polyfiller then sand.
Sand woodwork / radiator to "scuff" the surface - makes it easier for new paint to cling to.
Paint the woodwork and radiator first.
Then the ceiling - magic white is good because you can easily see where you have gone over. Work in 1m squares and move fairly quickly - don't go back over an area once it's started to dry otherwise you'll lift the paint off. Roll in one direction e.g. forward and back, then go another way e.g. side to side or I prefer diagonal.
Then move on to next 1m square. Generally I find one coat on the ceiling is fine.
By then your woodwork should be touch dry - does it need another coat? If the original paintwork was yellowing you may need two coats. Otherwise one may be enough just to freshen it up.
Walls - do one wall at a time. Use a paintbrush to go round the edges of the wall. Where you then have a line of paint on the wall, feather it in so when you roller over you don't have a line showing. But hard to describe!
Roller in the same way as the ceiling - 1m squares, two directions, work quickly.
Next day check the walls - do they need a second coat? Second cost IME doesn't use as much paint as the first coat.
For a small room, I do all my prep on Friday night. Woodwork, ceiling and first coat walls on Saturday. Second coat walls on Sunday, then tidying up and putting furniture, lampshades, curtains etc in.
In between Saturday and Sunday, wrap your roller in cling film. Then you can use it again for second coat. I just bin afterwards because I find they don't wash very well. Wash all paintbrushes as soon as possible though.
There's a sticky blue covering sold in Screwfix that you can use to cover carpets. I find this better than dust sheets for the edges because you can stick it right up to the skirting. Then I lay dust sheets over the top as an extra protection.