To go to Graduate School, you must have high smarts and graduate from high school and college.
That said, start by creating a character until you have decent smarts of at least 40+. You can accomplish this by rerolling characters until you get one with around that level.
This number will also be fine enough, as you can increase this all the way to 100 by simply reading books or going to the or going to the library when it unlocks.
When you got the high smarts, age to the point where you finish High School, and then move on to college and choose either English, Psychology, or Math as your major.
After this, finish college by aging a few years, and you will be able to go to Graduate School by selecting the seek higher education option. If you don't see this tab, you can always find the option to go to Graduate School under the education tab in careers.
When you finish graduate school, you will be able to apply and get the following jobs under careers, all of which have decent salaries of 57k to 210k
- School President
- Asst. Superintendent
- Asst. Principal