Put your bike on your repair stand (for people that think they can get by without one, here is a perfect example of why you DO need one) so that you have access to the drive side of the bike. Shift the RD into the highest gear (i.e. - the little cog). Now, turn the crank with one hand and, with the other hand, push on the bottom/right of the derailleur parallelogram - this will drive the chain to the low gear (the big cog). Keep cranking. If you let the parallelogram go, the chain will shift back to the high gear (because that's where you have the shifter set).

The adjustment you want to make is the "L" limit screw. You want to set the low (= "L") limit screw so that your RD shifts smoothly to the low gear, but not beyond it. When you push on that RD parallelogram you want to push firmly. If the chain jumps off into the spokes or even starts to grind against them, you need to adjust the limit screw accordingly. Look down into the parallelogram and see what the limit screw does and what it stops against.

No need to shift through any of this. Just keep cranking - push the RD so the chain moves up the cogs - adjust the limit screw so you get to the big cog and not beyond.

While you are at it you might as well adjust the "H" limit as well. When you let the chain come back down to the small cog it should only get to the small cog and not beyond. When you are done with the limit adjustments keep cranking and shift through all the gear combinations and fine tune if necessary.

You can do these adjustments with the shift cable disconnected if you want. Cable tensioning for index shifting and "B" adjustment are another issue.