In the choose email signature (View) screen, you can tap on the Edit button at the top of the screen to edit signatures. Now tapping on a signature will open the edit screen instead of selecting it.
You can use the "+" button to create a new signature and edit it.

To delete an email signature, tap twice on the delete button to the left of an email signature when in edit mode.

Signatures can be edited much like emails. Tap to select text and then you can choose several formatting options in the text popup menu.
On the iPhone/iPad, you can also do a long tap in the text area of the signature to show the menu and tap on the image button to insert images from your photo album.
For a Mac, right click and select the "Format" menu - "Insert Images"
Images can also be copied from other sources and pasted into signatures.

Once you have added the image you can pinch the image with two fingers to resize it. Double tap on the image to change the image file size.

Tap on "Format" to see all of the advanced features, such as color, font, size, inserting images and adding web addresses behind text. Tap on the right arrow in the menu popup if the "Format" button is not visible.

The action menu in the top right will allow to change to the default AltaMail signature and will also revert to the original signature and remove any changes.

Advanced users can choose "Show Source" to edit the HTML formatting behind the signature. This will also allow you to resize images. When this editing is complete, select "Preview" from the action menu to view the changes.