CSAs are a very simple agreement between you and a local farmer. You pay an upfront "subscription fee" directly to the farmer and each week during the growing season, the farmer packs a "farmers-market-in-a-box" just for you (usually mid-June to late-October). The money goes directly to the farmer and the food goes directly to you.
Each farm's CSA program is slightly different. Read more about factors to consider when choosing a CSA - 1.2 MB pdf