Generally you need a crypto wallet, such as MetaMask, and you can connect this to the game's website. Even if a game is free-to-play you'll need to connect a wallet as these games will still offer free token rewards. As a rule these are the easy steps to take:
1. Create a crypto wallet, MetaMask is a universal one, and then purchase Ethereum.
2. You'll likely need Ethereum even if a game uses its own token.
3. Connect your wallet to the game's website and purchase your NFT.
4. You can also purchase a game's NFT in OpenSea and hold it in your wallet.
5. Play the game, earn and develop your NFT hero or creature.