Does anybody know an easy way to clean the derailers and chain on my bike
"Easy" is a subjective term. I consider it pretty "easy" in that it's not complicated, but it can take some time to really "do it right" in my opinion. I don't do a "full" cleaning after every ride, but I'll at least brush and/or rinse the chain off and lube it after most rides since I usually get into some water and a bit of mud.
MTBR actually offers a "how to" on drivetrain maintenance. The article differs a bit from my personal regimen, but it's a good starting point. Here's the link: MTBR Guide to Drivetrain Maintenance
Regarding the article's suggestion to not lube before the chain is completely dry, it should be noted that some lubes (such as Boeshield) are water displacers. With this type of lube you actually CAN lube the chain even if it still has a bit of water on it since it will displace the moisture (although it's still best to "try" and get the chain fairly dry.) I personally think it's better to get this lube on the chain quickly rather than waiting for the chain to completely dry since this will lower the potential for rust.
The guide should get you pointed in the right direction, however I'll add my little $0.02. One thing you can do to make cleaning the drive train A LOT EASIER isd to purchase a SRAM Powerlink and install it on your chain - doesn't matter which brand chain you're rusing it works on them all. Then it's as easy as sliding the link towards each oither and off pops the chain for easier cleaning AND it also makes it easier to clean the cassette, derailers, chainrings etc.
is it ok to use Mineral Turpentine on the Drivetrain
Dunno about Turpentine...it may attack some of the plastics/paint on your bike.
I have recently started using Finish line's degreaser on my chain & gears. Its safe on ALL surfaces (according to them) and is biodegradeable. It really works good to dissolve all the old gunky lubricant & start fresh with each cleaning.