If you've found a wild patch of the most delicious raspberries in the world, then you may want to save a few to start your own raspberry patch. Planting raspberry seeds may take longer than picking them up at the grocery store, but raspberries can be expensive and are nutritious. Once established, they grow well in temperate climates and spread easily.
Choose a nice, plump and flavorful variety of raspberry. Avoid commercially grown raspberries, since seed breeders sometimes breed fruit with sterile seeds. Additionally, fruit that's picked for food isn't left to mature on the vine long enough to be fertile.
Smear the fruit on a paper towel and allow it to dry in the sunshine. Rinse the sugary pulp off of the seeds by spraying the paper towel and lightly scrubbing them. Allow them to dry again, then shake them into an envelope.
Place one seed in the middle of a small pot under an inch or so of compost. Firm them down, then simulate a winter by storing it in a cool, dark place. Let the soil be moist-dry but not too wet. You don't want the seeds to rot. Planting one seed in each pot ensures that you won't need to thin them.
Use a cold-frame to transplant outside in mid-spring, allowing them to "toughen up" before being exposed to possible freezing temperatures. In the meantime, transplant to larger pots if necessary.
Expect two flourishes of fruit per season for some varieties. Old wood will fruit first, and the new shoots will fruit later in the season. During the first year, there will be no old wood, so you'll end up with less fruit than you can expect in later years.