Pinch off basil leaves when they get large enough (the more you pinch it off, the more it grows). Discard stems and wash leaves. Either spin dry in lettuce spinner or lay out on paper towels or a kitchen towel to get excess water off. Put a few handfuls of basil into food processor using the steel blade. Bowl should be full but not tightly packed. Pulse, while drizzling extra virgin olive oil (EVOO) into feeding tube. Pulse until coarsely chopped. Make sure all basil is well coated with EVOO as this keeps it from turning dark in the freezer - 2-3 Tablespoons per batch should do it. When I put chopped basil in the container, I added a little more EVOO to make sure it covered all the leaves. If you want it for a vinaigrette, use more oil and chop finer. Use small containers with tight fitting lids. I used those plastic containers that baby fruit comes in, they were perfect for the right amount for a recipe. I used them all winter and they were just like fresh basil, no turning brown and tasted great in pasta dishes, etc.
NOTE: If you have some of the old pop-out ice trays, you may want to try this: Put a little EVOO in bottom of each pop-out, place some coarsely chopped basil into each pop-out slot, drizzle a little more EVOO over to make sure it's all coated. Place ice tray into the freezer. When frozen, pop out frozen basil (it may need a little help with a table knife) and place each frozen "cube" into a gallon zip-lock bag. Place bag in freezer and keep adding to the bag until you have as many as you want. This winter when perparing your dish and you want to add some basil, remove a cube from the bag and add to your dish. It's delicious and already has EVOO, too.