Alex,

You can accomplish this by inserting fields into your document.  The
forms tool bar will allow you to insert the appropriate fields. After
you can completed entering the form fields, highlight the padlock (it
is the last button on the forms toolbar).  This will lock the form and
only allow the fields to be editable.  You can navigate from field to
field using the tab button.

To handle the underlining, I typically lay my forms out in tables and
use the borders to act as the underlining.

Hope that helps.

What you are describing is a protected form. You do need to set this up as a
template so that each user creates a new document based on the template and
fills it out. See
http://word.mvps.org/FAQs/Customization/FillinTheBlanks.htm and especially
the forms tutorials by Dian Chapman that this article links to. If you put
your form fields in table cells (recommended), you can apply a bottom border
if desired.