There are a couple approaches to exploring farmer's markets; you can just find a good one, show up and see what's new, or you can be "in the know" on what is in season for your area so that you are assured you are buying local produce.
The first approach is kind of "Iron Chef" fun, you just go out and happen on whatever is in season, then plan menus. The second approach lets you plan ahead and be more informed about your purchases. For example, if it is late July in the Midwest, and you see spinach on the table, it is likely not grown local. This kind of information can help you purchase wisely and purchase only local, in season produce.
Many farmer's markets require the farmer's to mark the produce to indicate whether it is locally grown or not. But this is hard to enforce, and the signs can be easily missed in the crush of a busy market.
If you want to know what's growing, there are a lot of resources online to view a calendar of what is in season for a given area. Here in the Midwest, you can find such calendars for the Greater Kansas City region, and here is one for the St. Louis and Illinois region.
It also helps to get to know the farmers, and find the reliable ones with the best produce that you find yourself buying every week. Look for clear indications that they "sell only what they grow."
Many areas have a local food circle of recognized farms who participate, another way to be sure you are getting the real local crops.
We participated in a CSA in the past years, but could not keep up with a child and the amount of produce to prepare, eat or freeze. I thought I was savvy after that experience, but I think I have learned more than ever participating in this year's challenge. It's been an amazing experience.

