You can use the Metamask browser extension. Polymarket runs on a token called USDC, which you can buy from Coinbase for US$1 a pop with no fee (and also sell it back for $1 for no fee).

I used to use Polymarket a lot because it was previously filled with crypto bros and MAGA idiots who would vastly overvalue stupid bets (like "Will Canada join the USA") and provide easy money. But I haven't used it for a while, so I don't know if that's the case any more.