Green Manure: On plots where people dig their soil, green manures would be dug in so that they can release the nutrients for the next crop. To use them in a no-dig system, they are either cut down or left to die back then left as a mulch on the soil surface. They may need to be covered to help them break down more quickly. -source

Clover grows best in poor soil; so to help it compete well with the grass, you would not directly fertilize your turf. Instead, use a mulching mower; the pulverized, nitrogen-rich grass clippings (and in your case, the even more nitrogen-rich clover clippings) these specialized mowing machines return to the turf will give your lawn—including the clover—a gentle feeding every time you mow.

There are three true members of the clover family: White (sometimes called 'Dutch clover'), Red, and Crimson (yes, Tommy James & The Shondells fans, there really is a Crimson Clover).
Alas, Crimson clover would not make a good lawn; it's an annual plant that dies at the first frost. But it's a dramatic one-season plant, growing up to three feet tall with beautifully colored blooms that attract lots of pollinators and beneficial insects. It's used by farmers—and savvy gardeners—as a green manure/cover crop. Its deep roots naturally aerate the soil, and after it dies, the above ground growth is either plowed under to nourish the following year's crop or just left on the ground to release its nutrients slowly without any tilling.

Red clover is biennial—a plant that lives for two seasons. It grows tall—two to three feet—grows fast, loves cold, hates heat, does not attract pollinators and grows in the worst soils. It's also used almost exclusively as a soil- and drainage-improving cover crop/green manure.

White clover is the best choice to try and grow instead of a lawn or for seeding into a lawn. (In fact, white clover was a deliberate component of virtually all grass seed mixtures up until the 1960's.) It stays fairly low (topping out at around a foot), can be mowed just like a lawn, handles foot traffic better than the other clovers and tolerates summer heat better. But, like cool-season grasses themselves, white clover still doesn't like hot summers, and may need a lot of water to survive them. (Typically, clover needs more water than lawn grasses.) It's also slow to establish; and although 'technically' perennial, isn't very long lived. That means—like the shade-tolerant cool-season lawn grasses—it should be over seeded or freshly seeded every couple of years. The flowers do attract bees, so sting-allergic people should avoid it and the rest us should not go barefoot on it.

Because white clover does behave so much like a cool-season grass, I suspect it would do also best when the seed is sown in late summer—when the heat is abating but the soil is still warm. (As with the cool-season grasses, Spring sowing require you to wait until the soil temp is at least 60 degrees; and by then, stressful summer heat is generally right around the corner.)

To help clover be a lawn rather than just be a part of one, you should add as little direct nutrition to the soil as possible. Clovers have the ability to form a symbiotic relationship with soil-dwelling bacteria that enables the plants to take plant feeding Nitrogen out of the air, and so they kind of feed themselves. (To make sure that this 'nitrogen fixation' takes place, purchase a clover-specific inoculant and use it at planting time.)

To start out relatively weed-free (with a big tip of the YBYG hat to the guy at Lowe's who bad-mouthed chemical herbicides; he's my new hero!), make a 'stale seed bed'. Till the area about a month before planting time (which is ideally mid-August for both white clover and the cool-season lawn grasses), rake away as much of the old green as possible, level the soil, water daily to encourage all of the weed seeds you uncovered and then planted to sprout, and then slice off the resulting weeds with a sharp hoe two weeks later.

You should then be able to sow your inoculated clover seed, cover it with weed-seed-free top soil and have a good start on a clover-ishous lawn! - source