Staking starts by storing coins in your wallet, which needs to be online. Once your coins reach maturity, you can begin staking by opening your wallet and unlocking it for staking. Your wallet will then start competing with other wallets for signing the next block. As a reward for keeping the network secure, every minute one online wallet is chosen to receive a stake reward based on the coins they own.
If you are chosen to sign a block, you will get a staking reward. After this, the coin age of those chosen will be zero, and will have to mature again. There is no minimum amount needed to stake LYRA, but having more coins staking will give you a larger weight, and therefore a higher chance to receive the staking block reward.
Generally speaking, PoS is solving the same hashing problem as PoW, but hashes are built from Coin Age and existing UTXOs (Unspent Transaction Outputs) not from running a mining rig.