1. Go to Settings--> Accounts
2. Click "add account"
3. Select Google as the type of account
4. Select that you wish to Add an "existing" account
5. Enter your email address and password (ex. firstname.lastname@example.org)
6. Select what you want to sync to your phone (most likely only mail).
7. Once setup finishes, you can then read from both accounts in the Gmail app. Switch between mailboxes by clicking the envelope icon in the top left corner and then selecting the account you wish to read.