WalletConnect is the web3 standard to connect blockchain wallets to dapps.
Start with Connect button and pick a WalletConnect as a method.
At this step, you will be able to choose a network of connection
If you want to switch networks - you will need to disconnect your wallet and do the same steps with picking a new network.
Wallet connect supports a large amount of wallets, just find it in the upcoming menu
Also, there would be a confirmation of wallet connection to Dapp.
After confirmation in your wallet-app just come back to the browser.