How do I insert a "text form field" within my documents?

I generate test and exams for an online Bible college, and I need to insert text from fields for each test question asked, for students to record their answers in.

I am not really sure about what you want to. May be this is what you need. I assumed you will use Writer. Then this might be what you are looking for:

Adding Input Fields
An input field is a variable that you can click in a document to open a dialog where you can edit the variable.

  1. Choose Insert - Fields - Other and click the Functions tab.
  2. Click “Input field”in the Type list.
  3. Click Insert and type the text for the variable.
  4. Click OK.

To quickly open all input fields in a document for editing, press Ctrl+Shift+F9.

I recommend to have also a look into the manual:
https://wiki.documentfoundation.org/Documentation/Publications