I have a questionnaire on an Excel spreadsheet with 20 yes/no
questions. What is the best way to create a spreadsheet with the option
of a "yes" or "no" box that can be checked one or the other exclusively?

One easy way is to use data validation. The user sees a pull-down list for
each question -- not a check box -- so it’s not exactly what you asked for.

Select the cells where answers should go and use:
Data Validation

In the “Settings” tab, choose
Allow List
For the “Source” put
Yes,No

If you want to get more elaborate, fill in the “Input Message” and “Error
Alert” tabs too.

Note: using “Error Alert” you can stop the user from typing in an erroneous
value but you can’t stop the user from pasting one in.