I use quick links so that I can remove the chain easily. If the transmission is really bad I remove the lot, well most of it.
Chain and cassette off and wash in a tray of white spirit, you need to shoogle the chain about quite a bit and use an old toothbrush to get the crap out of the rollers.
Wash them both it water with a little detergent to get the last of the white spirit off and stick in the oven for a few minutes to dry the water out.
I clean the chain rings and front dérailleur on the bike, just wiping them down with some white spirit on a rag.
The rear dérailleur I'll take off to clean if it's really bad but usually I just take off the jockey wheels, clean them out and clean the rest on the bike.
Put it all back together with a drop of Finish Line Cross Country on each link of the chain and a drop on each dérailleur pivot. Now and then I also run a drop of Cross Country down the inside of the cable outers.
That's what I've done for years and it works for me :0)