How to save seeds.

This is something I'm asked fairly often, so hopefully this will be helpful.  This is the method that has worked best for me, after much experimenting.  If you have any questions, feel free to ask!

 Step 1:  Select your nicest fruits and veggies for seed.

Make sure your selection is an heirloom or open pollinated variety, not a hybrid.  A hybrid is a cross of two or more other varieties; sometimes their seed is sterile, but most often you end up with one of the parent varieties.  Most of the fruits and veggies sold at grocery retailers are hybrid, so you'll want to avoid saving seed from those.  If you aren't already growing something, start with fresh seed.  Johnny's is a great source.

Step 2:  Gently remove the seeds from the fruit.

 Step 3:  I use these mini strainers for small seeds. 

They are very handy, and can usually be found pretty cheap.  I got mine in a two pack from the Dollar Tree. 

 For larger seeds, you can use a regular colander, or even a fry basket.

Step 4:  Because nothing is ever as easy as it should be, and gardening is messy business, seeds are usually covered in some type of slimy glorp.  Or maybe just something that wants to be tomato sauce when it grows up.  Either way, you'll want to rinse that off the seeds.

 Step 5:  As I said: Messy Business.  I push the slimy glorp through the sieve while rinsing.

 Step 6:  I place the strainer on a paper towel to drain, and place in a warm (but not over 90 degrees Fahrenheit) and dry location.  The kitchen counter works well for smaller seeds.  I put bigger stuff on a rack near the back of the wood stove, where it doesn't get very hot but does stay warm and dry.

Attach a label of some sort to your seeds!  

You may think you'll remember what they are, but all tomato seeds look alike.

 Step 7:  A lovely chunk  o' seeds!  Tomato seeds tend to darken as they dry, so don't let it worry you.
Crumble the seeds apart, gently, into a paper bag.

Step 8:  LABEL LABEL LABEL that bag!!!

I like paper bags for storing seeds.  Store in a cool, dry place for next year's garden. Or, store in the freezer for long term storage. 

This method works well for most fruit and veggie seeds.  Lettuce, radishes, rutabaga, and many others, produce their seed in a pod after flowering. For those, I let them dry on the stalk and then pick them, place in a paper bag, and label.

Beans, peas, and corn can also be saved by letting them dry on the vine/stalk, then storing in a cool, dry place.  Corn should be husked before storing.  Beans, in my experience, do just as well whether removed from the pod or not, as long as thoroughly dry.  Do not harvest dried seed when it's wet outside, unless you are going to let it dry thoroughly before storing.

 Flower seeds are pretty much the same.  The center of the flower is usually the seed head, and once the petals fall off and the seeds dry, they are easily collected.

Be sure to do a little research on whatever variety of seed you choose to save. Some seeds require stratification, which is simply a way of simulating the winter dormancy to stimulate germination.  For the most part, you won't have to worry about this with the basic veggie garden seeds.  Lettuce and strawberries are the only ones I can think of offhand that require stratification.  You can accomplish stratification by putting the seeds in seed starting mix, in a bag, in the fridge or freezer (be sure to research the time and temps for each type of seed).  When you order seeds, the packet should say if stratification is necessary. In most cases, it's been done for you.  If you choose to store your seeds in the freezer, you don't have to worry about stratification.

There are other seeds that require almost no work at all.  Tomatillos, for instance, tend to volunteer all over the place.  I have about 30 plants this year, and I didn't plant any of them. Either they volunteered, or the garden gnomes were very busy this spring.  To save those seeds, I just leave a few fruits outside.  The fruit part rots away, and the husk makes a neat net to hold the remaining seeds.  I'm hoping for the same results with ground cherries (husk cherries), but as I've never saved those seeds before, I'm trying both methods to ensure viable seed for next year.

Remember, not every seed you save will be viable, which is why plants produce so many of them.  Save more than you think you'll need, just to be sure you have enough.  If you end up with extra plants, you can always share them with friends.

ETA: I use the paper towel method (see comments) for tiny seeds that would slip through the strainer, like ground cherries, sweet pea tomatoes, tomatillos, etc. For bigger items, I prefer the strainer just to cut down on the fruit flies and smell of old produce.