This is the slower part of the year for gardening and this makes it a great time to harvest seeds. Seeds packets are not horribly expensive but the prices go up every year and saving seeds will help alleviate this issue.
I started saving seeds a few months ago and still doing it. These are not only meant for home-grown vegetables and fruit but may also be done with store bought produce. It must be noted though that store bought produce may be a hybrid and may not grow correctly. This is why growing "heirloom" fruits and vegetables is important as these will produce the same every year.
There are a few basic instructions that should be followed and may be different depending on vegetable or fruit. I found many websites with instructions and here are some to get you started. If you are looking for a specific fruit or vegetable, just do a search on how to save seeds from it. These may be a bit overwhelming but offer great information.
1. EHow Article
2. Mother Earth - Mother Earth also has a wonderful magazine that covers many topics for gardeners.
3. GardenWeb forum for seed saving
I will let you go through it at your own pace and hopefully get something out of it.