To start, open either the Email app or Gmail app, depending on which one you want to change. Next, tap the More button in the toolbar. It's represented by three dots: in Gmail, it's in the upper right; in Email, it's in the lower right. Next, select Settings from the menu that appears.
On the Settings screen, tap the email address whose signature you want to change, and on the following screen, scroll down and tap Signature. Enter the signature you want to use with that account, then tap OK.
If you have multiple email accounts you want to append signatures to, go back to the main Settings screen by tapping the Back button in the upper left corner of the screen. Select another email address from the list, and repeat the process.