To participate in Hop governance with your HOP tokens you need to first delegate your voting power to yourself.
This requires an on-chain transaction and costs some gas. If you prefer you can also delegate your voting power to one of the existing delegates.
Once you have delegated you will be able to vote for the next governance vote.
Both actions can be done here: https://www.tally.xyz/gov/hop
Currently you need to hold the tokens on Ethereum as Hop uses the same governance contracts as most DAO's like Uniswap, ENS, Compound etc.
However, multichain governance is an active area of research.