Q: how to check Mail from a different computer

Depends on what your e-mail provider provides.

Some like Gmail, you can use the computer browser.

Otherwise you need to create an account on that computer e-mail client.

Are you referring to Apple Mail via iCloud? If so, then go to iCloud.com on any computer and sign in with your iCloud ID. You will see the Mail app there, and can open it to check you mail at any time.

Cheers,

GB