Well it depends entirely on the species you are talking about. Some annuals such as marigolds and zinnias are best saved by keeping seeds from mature seedheads. However, this may not work if you are growing hybrid varieties. Those tend to be sterile so you can only enjoy them till frost. Others such as impatiens, geraniums, and coleus can become houseplants, but you need to take fresh cuttings in late August and start new plants. Digging up plants from outdoors rarely works. To take cuttings, just take a several inch cutting from your plant, strip the lower leaves and root them in water. Then, when the roots are a few inches long, you can pot them up in houseplant potting soil. With geraniums, some people have luck digging the entire plant and hanging them upside down in brown sacks in the basement over winter. I've not had luck with this system since it depends a lot on how cold or warm your basement gets. I think you're better off making cuttings and keeping the plants alive on a sunny windowsill all winter long.