There are four story chapters, each with 30 stars in total to get. These are ( In Order )
World's Fastest Rentals
There is a potential of 120 stars to get in total, so don't feel like you need to achieve 3 stars on each one.
Aside from practice and personal skill, the only two tips I would give are:
1. Never use the 'next chapter' option when selecting a race/mission. Always use the 'Chapter Select' option as this will outline exactly what you need to get 1, 2 or 3 stars and is - as far as I can see - the only way to find this information. At the very least, it will give you an idea of how close you are to the next star.
2. Don't get hung up on getting the 3 stars if you have been trying for a while. As mentioned before, you don't need to three star every chapter, so if you've been banging your head trying to get a three star in a race, just move onto the next one. You can afford some 2 and 1 stars in there.
Thanks to Comrade Spanner and pezboyben for confirming that the new "British Racing Green" chapters which have been added also count towards the total, meaning you have even more room for error now!