I'm intrigued by the primary use of cover crops to enrich the soil without tilling. I'm also interested in incorporating a no till system.

How would you convert a plot of grassy weeds into garden space? I would use a hoe and clear all of the weeds out, cart them away and compost them if I had a heated pile going. Then I would sow the seed of an annual cover crop into the heavy clay soil I have (not sure what cover crop I'd use. Maybe annual rye grass or oats I've read is good) in the spring. I live in the deep south so I don't know if winter killing would be optional. So I'd probably use a scythe or a mower to cut them in place before fall and then leave them on the ground to rot. I would then cover the rye grass with compost and sow fall vegetables in the compost. That would be my ideal way to begin my bed. I'm curious if this would work.

Also how important is it that the cover crops be annuals? I've read of using clover but I know this is a perennial but I'm not sure how it grows. Does it just reseed itself or is it just not winter killed? Also I've read of growing vegetables with clover as a living mulch. What is your opinion of this? I imagine the clover would compete with the crops and there wouldn't be significant growth in the vegetables.

Thanks for the great questions, Jalen!  My favorite way to convert a grassy area into garden without tilling is to use a kill mulch (aka a sheet mulch.)  You can read the long version in the May volume of my ebook series (which I'm emailing you a copy of), but the short version is that you lay down a few sheets of damp corrugated cardboard to kill the grass, with compost above and/or below, then top the whole thing off with mulch.  If you've got time to leave the kill mulch on for a summer before planting, you'll then be able to grow anything you want.  If you're going to plant into your kill mulch immediately, I recommend putting a good layer of compost on top of the cardboard and seeding only shallow-rooted crops your first year.

While your method would work (especially if you used a shovel instead of a hoe), it would really amount to tilling and you'd lose a lot of the organic matter right at the soil surface.  Granted, your cover crop would replace some of that.  An annual cover crop that works in the summer is buckwheat, which can easily be killed using a mower, weed eater, or just by yanking the plants out of the ground and laying them on the soil surface once they're in full bloom.  (Buckwheat's not a big fan of clay, though.)  A problem you might run into if you used a grain instead (generally planted in the fall) is that the more woody plant matter would suck nitrogen out of the soil as it decomposed, so you might end up with hungry vegetables unless you added a lot of compost.  I like to rake oat leaves back in the spring, add my compost and plant my seeds, and then bring the oat mulch back up around the young plants as they get big enough to handle the occasional oat straw leaf blown out of place.

To answer your question about annual vs. perennial cover crops --- annuals have a big advantage in no-till systems in that you can often find a way to kill the plants without impacting the soil in any way.  Perennial cover crops are generally tilled into the ground (although you can also lay down a kill mulch over top of them after mowing the cover crops close to the soil.)

There are several types of clover, some of which are annuals and some of which are perennials.  The primary annual clover is crimson clover, which is generally planted in the fall in the south, overwinters, and then is killed in late spring or early summer as it begins to bloom.  My father (in South Carolina) has let his crimson clover go all the way to seed, at which point it dies back naturally, then he plants into the mostly bare soil and lets the clover come back from seed in the fall.  He does till his garden every year, though, so I'm not positive this system would work with no-till.  (In my own garden, I find that crimson clover doesn't keep back weeds very well over the winter.  In general, grain cover crops are much better at suppressing weeds and adding organic matter to the soil while legume cover crops are best at providing a quick dose of nitrogen.)

I believe Steve Solomon is the one who wrote about growing white clover between the garden rows as a living mulch.  White clover is a perennial, so it will keep plugging along unless you rip it out by the roots.  Solomon's method involved mowing the clover often enough so that it didn't compete with the vegetables, allowing the high nitrogen clover leaves to mulch and feed the garden, along with the high-nitrogen root nodules that are shed by the clover when it is mowed.  I didn't mean to follow Solomon's lead, but in one of my garden areas, white clover naturally sprang up in the mowed aisles between my beds, so I gave a variation on his method a shot.  In my garden, at least, the living mulch system is problematic since my aisle clover tries to run into the vegetables' space at every opportunity and I spend a lot of time ripping it out.

You mentioned in your email that you are seventeen and that your parents aren't into growing vegetables --- I hope you're able to find space to give some of these ideas a shot.  The best way to learn about gardening is to get your hands dirty and try things out.  You'll soon discover what does and doesn't work (and will have fun in the process.)  Good luck!