I have always just tied bundles of basil together and hung them upside down to dry in the late summer heat. This year I am freezing it two ways; as a puree in oil and slightly changed up for pesto. For the strait basil and oil puree, wash and dry a big bunch of leaves. Fill up your food processor bowl and pulse until leaves are finely chopped. Add 1-2 teaspoons olive oil and continue pulsing until oil is evenly distributed. To freeze, either put in plastic freezer bags and lay flat in freezer or freeze by the tablespoon in ice cube trays and transfer to freezer containers.
1/3 cup pine nuts
2 cups firmly packed basil leaves
1 Tbsp freshly squeezed lemon juice
1/2 cup extra virgin olive oil
Place nuts in a food processor and pulse 2 or 3 times. Add basil and pulse a few more times. Repeat step with lemon juice. While running the food processor, add olive oil a little at a time. Scrape down sides and process until pureed. Place mixture into a quart sized freezer bag and seal bag, pressing out excess air. Freeze lying flat.
*note - I didn't have any freezer bags and I am in the process of switching from plastic to glass, so I froze mine in a small glass jar.
When ready to use add:
2 Tbsp chopped fresh garlic
1/2 cup freshly grated Parmesan cheese
If desired, 1 Tbsp freshly squeezed lemon juice
Puree into thawed basil mixture. Season to taste with salt and black pepper.