Before I got my Foodsaver I put leftovers in ziplocks, I just squeezed as much air as I could out of them then put in the freezer. Food will keep for months like this and I've done it for years.
You can take it one step further by using a drinking straw. Close the bag around the straw, then use the straw to suck all the air out you can. Once you've got it compressed down, pull the straw out and close the rest of the bag off as quick as possible (and breathe out quickly whatever you just inhaled). With a little practice you can get a lot of the air out pretty effectively. It can actually be done without the straw, but that's a more advanced skill. Call it the redneck's Foodsaver.
I am not an expert, but I use to put the meat in a zip lock and then lower it into a big bowl of water. Do this slowly..just lower it until you reach the top of the bag and ....zip, it.
