Actually I kind of got started the way you would- I have too many veggies to eat right now and want to keep some for later. I only remember my mom canning twice- she made tomato jam once when I was little and pickles one time when I was in high school. She wasn't that into it and neither were my grandmothers.
The best way to get started is to get yourself the equipment now. Once the produce is rolling in you need to be able to get it put up right away. If you already have the equipment then it's much easier to dive right in.
Get a boiling water canner (a large enamel pot with a removable rack) a jar lifter (kind of like a sideways kitchen tongs) and a dozen pint jars with lids (they come that way). All that stuff is usually available in your local supermarket or Wal Mart. But get it now because Wal Mart especially runs out of stuff quick.
Once you have enough produce to make a batch you need to set aside a few hours to process it. Get yourself the Ball Bluebook or the USDA Guide to Home Canning for some recipes and they will tell you how much you need. Usually it's a lot more than you think you will need in order to make a batch (like for 6 qts of spaghetti sauce I probably use about 30 lbs of tomatoes), so plan accordingly.
You can also visit Ball's website for a tutorial.http://www.freshpreserving.com/pages/preserve__fresh_preserving__home_canning_/33.php
If you want to can things like tomatoes (I cook them down into spaghetti sauce first) or applesauce they are considered high-acid foods and don't need any additional "preservative" ingrediants. Other veggies, like green beans, peppers and cukes need to be pickled in vinegar to preserve them. There are recipes for these in any canning guide and I usually make pickled hot & sweet peppers and cucumber pickles every year.
You must do this all in one day because for safety's sake the pickled veggies need to be "packed hot". You need to heat the vinegar/water/spices brine to boiling and pour it over the veggies you have already put into a sterilized jar (I put them through the dishwasher and then boil them in the canner as the water heats). Then cap the jars and boil them for the prescribed amount of time.
It's really not hard as long as you make sure you do all the steps in the right order and make sure you have everything ready. It's kind of chaotic and labor-intensive but in the end you will have a much better product than you could buy in the store and you will be proud you did it yourself!