Ditto what's said so far - take the scope off, take the barrel/action off the stock (very simple), dissassemble the firing pin from the bolt (if it's a mod. 70, it's very easy. other actions, I don't know).

If you're at all in doubt, call your local gun shop and ask them if they can take care of a thorough cleaning for you. My local one offers such a service. Althoug I've never done it, I could imagine circumstances where I'd be glad to have a major cleaning done by a pro shop (time, hassle and expertise factors).

Reminds me of a fall evening on a river in the middle of nowhere when my buddy and I spent about an hour holding the canoe in a very strong rapids/current while we fished for his .308 using a heavy spoon and fishing pole. Finally got it. Ruined his stock and cheapo scope, but the barrel and action were fine after re-hab. He replaced with synthetic stock and a good quality scope and had an upgraded gun to show for it.