The important thing is it to keep it smooth. The worst mistake you can make in golf is to try and follow where the ball has gone too early in the swing as it is likely to mean you move during impact.
You might not think your follow through is important. After all, the ball's already history. But if your follow through is right, you'll know you have a good swing. Visualise 'throwing' the club head ...
The best way to record your golf swing depends on your goals and budget. For a simple, budget-friendly approach, prop your phone against a stable surface or use a tripod for a more reliable setup.