Home canning can be the most frugal way to preserve the bounty from your garden, sales from the grocery, or meat from hunting. It doesn't rely on electricity and you know exactly what you are eating because you processed it.
I'm not going to give instruction on how to can, but I can recommend some books with reliable, easy to understand instructions. When buying equipment get the best you can afford. This will save you money in the long term. Start with a water bath canner (for jams, tomatoes, fruit and pickles), then graduate to a pressure canner (for nonacid vegetables and meat). Adding a box or two of jars will allow the recipient to get started canning right away.
Here are some of my recommendations: