Making sense of U.S. assist. prof. salaries: gross vs net, 9 vs. 12 months
In the United States, the "academic year" consists of the 9 months that comprise the fall and spring semesters. This is the period during which you are formally employed by the university and receive a salary. These 9 months also define what salary you are essentially guaranteed. However, it is possible that you will also get a salary for the remaining 3 months; for example, if you have grants from a funding agency or from industry, or if your department runs a summer program and you teach during these months. You can inquire with the head of the department that made you an offer whether they run a summer teaching program, and what your chances would be to get an assignment to teach. In other words, your salary may be up to 4/3 of the nominal, academic year salary, but that is not guaranteed.

How much of this money ends up in your pocket depends on a number of factors that are hard to estimate without knowing more:


You can look up the Federal tax rate for this income. If you're single, I would think that you have to estimate a tax rate somewhere in the 20-25% range on your total salary, including the 6.2% social security tax. But it may be significantly less if you have family and your spouse is not working.
Some but not all states (and in some cases, cities) have a state income tax. You can also look that up. Many states use a flat percentage of your income, typically somewhere in the 4-8% range. I don't know whether that includes deductions for dependents.
Retirement: Most universities have switched to a 401(k) system where you get no benefits from the university after retiring and both you and the university instead pays into an account over the time of your employment from which you can later draw money in retirement. Depending on university and state, you will have to expect to pay 6-10% of your total income into this account.
Health insurance: If your health insurance has to cover only yourself, then you can expect that your employer picks up all or almost all of the cost. On the other hand, if you have family that needs to be insured, then you have to expect that your share of health insurance will be in the range of $500 per month (for only a spouse) or larger (if you have children).


So if you add all of this together, if you start with $100k per year, you'll end up with maybe $100k-25%-5%-8%=$62k in your pocket if you're single, plus or minus several thousand dollars. But it may be quite different if you had family, depending on the state you're employed in, and any number of other factors.