If the chain is thrown off into the back wheel when you change into bottom gear (the largest sprocket), then you need to adjust the "L" limit screw ("L" means "low", as in "low gear") to stop the derailleur moving too far towards the back wheel.
If your limit screws aren't marked then put the bike, carefully, into bottom gear and have a look at the screws: the bottom of one of the screws will be closer to touching the arm of the mech. than the other (when correctly adjusted, it will actually touch it).
To double-check, put the bike into top gear (the smallest sprocket) and look again: the other screw will now be touching the mech. (assuming it is correctly adjusted).
On some derailleurs you can't actually see where the screws touch, in which case you'll need to turn the screws back & forth to observe the derailleur for movement.
Personally, I find the Park Tools website useful for instruction on such things, but there are plenty of alternatives.
If you've been dumping the chain into the spokes, I suggest you inspect the spokes near where they enter the hub for damage; if you find anything significant, or are in doubt, take it to a bike shop for inspection.