Here are five tips I have learned in recent years that have made my laissez-faire gardening approach a bit more affordable:
Did you know that basil will root if you place it in a glass of water on a windowsill? I learned this tip from The Tidy Brown Wren a few summers ago. This is a great way to keep fresh basil at hand through the winter (and through the summer too, if you don't want to schlep out to the garden for a few leaves). I have even successfully transitioned these plants to potting soil indoors. Just be careful when it's time to transplant these little plants outdoors--they require a very gradual transition.
Here's another tip that even my seasoned gardener friends didn't know: The white portion and roots of store-bought green onions can be planted in soil and will continue to grow and regenerate green, edible shoots. (When you plant them, be sure to leave a little green above ground for photosynthesis.) I was thrilled to learn about this, as I have a bad habit of buying green onions, using one or two, and letting the rest rot in the fridge. This way, I can just snip a few green shoots with scissors whenever a recipe calls for them. They grow quickly, ensuring a long summer of pasta salad...and onion breath!

This tip may or may not save you money, but it will definitely save your sanity...and your hands. If you grow tomatoes, you have probably had the experience of cooking all day (and burning your fingers with tomato juice) only to produce 3 lousy jars of tomato sauce. Take heart! There is a much easier way to save surplus tomatoes. Gently wash and dry the tomatoes, cut off the stem end, and put them on a cookie sheet in the freezer. Once they are frozen, transfer them to a Ziploc freezer bag. The best part? For use in recipes, just rinse a frozen tomato under hot water and the skin will slide right off in your hand! Revolutionary, I tell you!
As a side note, the watermelon in the photo above was also grown in our garden. Watermelons are easy to grow from last year's seeds...if you live in North Carolina!
[Edited fall 2012 to link to my new how-to post]
Seed saving sounds like something that only die-hard plant propagators do, but I'm here to tell you that it is absurdly easy. You can find instructions on my other post here. Or, if you're even lazier than this, wait for last year's dropped seeds to pop up on their own as seedlings and transplant those microscopic marigolds to optimal locations.
The hydrangeas above are from my garden, though this picture is from last year--this year we have lush leaves and no blossoms, thanks to a frost. I learned how to propagate them from Manuela at A Cultivated Nest. If you have never visited her blog, you're in for a treat!
Happy (Cheap) Gardening!