To build a quarantine workout accountability SMS system, users need to create a Strava app and obtain an Access Token with the necessary scope. They then use this token to access their activity data from Strava's API. Next, they set up a Twilio account and create a new function using the Serverless Toolkit that uses the Strava API to compute the time and distance of their last activity. The function is then deployed to Twilio and configured with a phone number, allowing users to receive an SMS message with their workout details. Users can test the system locally or use it as-is, but note that Access Tokens expire after six hours and need to be refreshed periodically.