How do I know what size to make the base and petals?

The bases, petals, and centers in the Flower Toolbox are mostly proportionately sized to help you out. That said, flower making is NOT an exact thing. This is GOOD because there's lots of flexibility and wiggle room. You can have huge petals and a tiny base. The only real rule is that the bottom of your petal be smaller than your base's diameter, otherwise it won't fit. Some flowers will look best with a small base (like a daisy or sunflower) while others will want a larger base to give the petals more room (like a rose).

I am not giving you exact measurements on purpose because I want you to try and learn, and then try again until you are happy. Trying and experimenting is a HUGE part of truly learning. If I just tell you exactly what to do, all you're doing is following my steps. This is not meant to me a step-by-step tutorial -- you can find lots of those for flowers on my blog. And you're welcome to try one of those first if that makes you feel more confident to experiment. What I'm teaching in Design to Shine is meant to be a lesson is how flowers are put together and an opportunity to try your own shapes and sizes out to see how they interact. So I'm really try to encourage you to just try some things, cut them out, and see what happens when you put them together. 
If it helps to see, here are two of the flowers I made during the lesson: