You understand the guilloche and how it will fit the tools you have. You've practised the parts. You've laid out the pattern on your wood. Now it's time to get to work!
As a general rule for carving mouldings, repeat the same cut with the same tool for as long as possible. That way you'll get a consistent look and work efficiently. It can be quite tedious unless you get into the 'zone' and then the carving just hums along.
Beeswax: see here.