Sleeping Bag in a trash bag?

It's easier if you put the empty garbage bag in your pack first. Then the sleeping bag and sleeping clothes go in, close the garbage bag, put everything else on top, pushing down if needed to squish down the volume. Works like a charm.

Jeffrey,
Two fine points:
1) You want to be using a Trash Compactor bag. They will take days of serious abuse without tearing. A 'Tall Kitchen Trash Bag' will fail on day 2.

2)After you have stuffed in your sleeping bag and perhaps other fluffy clothes, squash all as much as possible, then twist or roll the excess bag, forcing air out as you go, and tuck the excess between the bag and the pack, but do not cinch-tie it. You want to be able to let the captured air slowly escape as you pack gear on top of it. Tuck the excess with the opening pointing down so rain water can't run in.

If you are at risk for a swim – a stream crossing – then twisting, doubling, and cinching is a good idea and you just have to take the time to get out as much air as possible.