You'll want some 'browns' to mix in with the clippings. Leaf season is coming around... pile up some leaves and run over them with your mower. Mix the shredded leaves in with the clippings as best you can.

You can use any source of 'browns'. Browns are mostly carbon... wood chips, fallen leaves, hay, straw, etc...

Greens, like fresh grass clippings, contain fairly high levels of nitrogen.The problem with trying to compost straight clippings is that they 'melt' into a stinky, messy blob lol. They will eventually compost on their own, but you'll better results by mixing them with the high carbon materials.

I think the recommended ratio is 1 part green to 25-30 parts browns by volume. Btw... you can turn green grass clippings into 'browns' by letting it sit on the grass until it is dried out and brown. Much of the nitrogen will gas-off into the atmosphere. However, most people want the lawn to look nice, and if it clods-up it can kill the lawn.

If you have too many clippings, then yes you can pile it up in an out of the way place, it will eventually compost on its own. But if you really want to put it to good use, then save an amount of clipping that will equate to a 'proper' ratio of your availability of browns as discussed above. The rest you can mulch back into the lawn.

To mulch the clippings without special mowers or blades; simply mow the lawn and allow the clipping to mostly spread out, trying not to let it clump (perfection isn't necessary, but you may have to remove, or lift up the plastic cowl that you'll find on many mowers. Just put the cowl back in place near windows, people, pets, etc...) Let the clippings dry in the sun. Then mow back over them. They will easily shred and 'disappear' back into the lawn. This will both, feed your lawn, and your soil. It works best in the heat of summer, but unless it's a very thick lawn, you can usually spread it out enough to not kill the grass any time of year.

You can also use red wrigglers to assist with the process and remember to add the browns