There isn't any hard-coded form stuff. zen_draw_input_field is a function defined in function/html_output.php.

It's full structure is
zen_draw_input_field($name, $value, $parameters, $type, $reinsert_value)
where $name is the name of the field and can be almost anything that you wish, $value (if set) is the initial value, $parameters is used to add attributes such as an id or class, $type = 'text' (usually) or 'password' (occasionally) and $re-insert_value would be used if the form was not processed for some reason.

In most cases you can leave the last two parameters off. The aim of the function is to output the entire html needed for an input field, and there are other functions in the same file such as zen_draw_pull_down_menu to draw other types of form field.