You can type ctrl+D to view the document properties (also available from the file menu). There you can see the "security" of the document. If the document does not allow modification, there isn't anything you can do. (This feature is often abused - I don't know why people think they need protect a form from being filled out, but the Massachusetts Bar application is a typical example of stupid security.)
If the document can be edited but just doesn't have fields, you can create fields with the full version of Adobe Acrobat (not Reader). It costs like $600, but you can go to their website and get a trial version. Then you can add fields and fill them out.
In the end, you might be stuck printing and using a typewriter or neat handwriting. (or messy handwriting, as I do to protest the fact that they locked the form)