Eggplant seeds should be started early indoors. I like to sow mine mid-March, the same time as peppers. They do best when provided lots of light and warmth, I've found using grow lights makes a huge difference getting them started.
Transplant outdoors after summer warmth has arrived, usually mid-June around here. Choose a site with maximum sun. Eggplants do best in fertile soil with plenty of compost, but don't over-do the nitrogen, which can lead to wild foliage at the expense of fruit. They don't require staking the same way tomatoes do, and are fairly low maintenance once they get going.
For seed saving purposes, you'll want to let your fruit ripen fully, well beyond their peak eating stage. Fully mature eggplant will usually turn a shade of yellow or tan, and will be noticeably less firm than they once were. If in doubt, cut a fruit open and check out the seeds; they'll be solid and brown when mature.
