There was a LCC giveaway on twitter that just ended. If you had LTC in a cold wallet at the time of the fork, you will have LCC waiting to be claimed.
there are some wallets like Coinomi wallet, Xeeda, the LCC core wallet client and the SPV wallet will be released soon. You can also store on the exchanges but it's never recommended to store crypto on an exchange iof you aren't trading it.
Current exchanges are listed here and HitBTC is confirmed and will list LCC after they have integrated it into their exchange and tested. https://litecoinca.sh/#exchanges
You can mine LCC the same as BTC. There is a #mining channel in discord where you can chat to pool operators and miners alike come along the community is great, much praise of how we treat people with open arms, we even welcome the trolls as we have been successful in changing minds of people giving the facts and being respectful to everyone
https://discordapp.com/invite/F2nZXnW