As I understand it, you need to purify it (remove all meat products from it by heating it over water to allow the meat and juices to drop into the water). Once you've done that, you just need to keep air away from it. Old fashioned lard cans just had real tight-fitting lids; they didn't bother with canning it. Tallow would be the same as the lard, wouldn't it?
Render the fat and strain into jars. It keeps for a long time. I usually store mine on the countertop or sometimes in the refrigerator. The colder it is, the longer it will take to go rancid. Even that's not dangerout---just unpleasant.
do like britesea says and render the fat over water (toss it all in a pan with water not in a double boiler) simmer it on low until all the fat has melted and the meat bits fall into the water and the fat is floating on top then skim the fat into jars, clean the rims, put the lids on and seal them. lids in simmering water too please. some folks will can them in a boiling water bath for 30 min for pints and 45 mins for quarts. kept in a cool dry place it will last for years. and please use a low fire to render the fat as to high of heat can cause a fire