To make a deposit and have your wallet address become active in the Tezos blockchain network, you must first conduct a transaction to the wallet. This can be done through an exchange, where you can purchase Tezos (XTZ) and send it to your wallet address. Once the transaction is completed, the account will be detected in the explorer and the wallet address will become active. After the first transaction is completed, you will be able to make additional deposits to your wallet address and the address will remain active.