please visit the official litecoin website at https://litecoin.org/ and follow the links and instructions.

you can run a full node by downloading Litecoin Core. which means it will take up a longer time to sync and download the whole blockchain and will take up space on your HDD (not sure how big is the blockchain on LTC).

or you can use the SPV wallet called Electrum-LTC which is a lightweight wallet, only downloading blockchain headers which is a very small file. but you won't get the full verification.
bitcoin.stackexchange.com/questions/4649/what-is-an-spv-client
https://bitcoin.org/en/glossary/simplified-payment-verification


there is also wallets for cell phones.