There are a few ways to buy/deposit ETH: Wyre, Transak, or Direct deposit. Please check out how you can direct deposit: How to deposit (receive) tokens to your MetaMask Wallet
Wyre and Transak are on-ramp third-party solutions that are integrated inside the MetaMask wallet.
To buy with them just click buy or buy ETH on the main screen of your MetaMask wallet, and you will be prompted to follow the procedure for Wyre, Direct Deposit on the browser extension. On mobile, it's usually Apple Pay(Wyre), Transak. Please note depending on your region these solutions may vary. For example, NY and TX states are not supported by Wyre/Transak meaning you won't be able to use them to buy ETH. Wyre and Transak need BitLicense to operate in these states. Please check all geographical restrictions for Wyre here.
If you are in any of these states, please check a Direct Deposit alternative. You can always check the exchanges that operate in your country here.
In case you have any issues while purchasing with Wyre please contact them directly at email@example.com / https://wyre-support.zendesk.com/hc/en-us/requests/new
In case you any issues while purchasing with Transak please contact them directly at firstname.lastname@example.org