There is a very good description of how to add a text field to the shipping page in Zen Cart 1.3.0.2 in this thread. However, line numbers will be different in version 1.3.5 and if you wanted to add a different type of field or add it to a different page, then you would have to adapt the approach.

In case it helps, I rate it least difficult to add a field to the shipping page and most difficult to add one to the confirmation page. Adding one to the payment page falls in the middle. However, whichever page you add your field to, the change will require a fairly high degree of technical and Zen Cart knowledge. It's not a change for the faint-hearted.