First thing to do is figure out how to remove the stock and the bolt. It is essential in cleaning a rifle as it is the only real way to expose the internals, especially on a 700.
First I run a cloth through the bore with Hoppe's #9. What I use for cleaning is a good spraying of Berryman's brake parts cleaner. I use a plastic brush for any built up stuff. Be sure it is part #1420 on the back. It is the exact formula as a well known (Gun Scrubber I think) gun cleaner and is a lot cheaper. They make 2 different ones so make sure it is part #1420. I then blow it clean with compressed air. If you don't have a compressor use computer canned air. You can let it air dry but it takes a bit longer. Then run your bore snake through the bore starting at the chamber end. Oil all of the moving parts with oil of choice. I use synthetic because it doesn't break down like regular oil. Wipe it down to remove all excess oil and I usually leave it out an hour or so and wipe it down a second time after it oozes out of crevices. I will then put it together, make sure everything is working properly and store it until I use it again.
I do not put oil in the bore before storage. Some people say the bore will rust but I've never had this problem.