Perennial seed should be spread at 10 lbs (5 kgs) per 1000 square feet. These amounts apply equally to overseeding an existing lawn and seeding new soil.
Depending on the size of your lawn, you may want to use either a push spreader or a hand spreader to spread the rye seed. Hand spreaders are typically used for small lawns that have large amounts of detail, while push spreaders may be best for larger lawns or new soil with larger open areas. [6] X Research source
If you’re overseeding an existing lawn, it might be hard to rake the seed into the soil. If you can’t rake an existing lawn, that’s fine. The existing growth - even if it’s short - should ensure the rye seed isn’t disturbed.
You may have to cut down the sod to ensure it fits into smaller spaces or staggers properly. Use garden shears to gently cut the sod pieces down to size. The sizing doesn’t need to be exact since you can fill the spaces in with soil, but it should be pretty close.