How much are taxes for a postdoc in the United States? I'm being offered a postdoc position at Penn State University.

The recent rise in salary sounds good (about 4000$/month), but I wonder taxes may be not included. Any help?
You will be taxed like any other employee in the US, unless you are in the US temporarily and the US has alternative tax arrangements with your home country (see below). Salary is always reported in pre-tax terms. Your actual take-home pay will depend on deductions for things like healthcare, and the taxes in your state. At the new annual ~$47k level for postdocs, you can expect this to be in the vicinity of $2800-$3000/month, depending on your marital status, dependents, etc.

There are many online calculators for you to figure this out, for example HR Block or Intuit.

It's possible that if your home country has a particular tax treaty (link to IRS) with the United States your tax situation may be different. If this is the case, you may want to adjust your tax withholding accordingly, though you may also owe taxes to your home country. If you have taxes withheld that you do not actually need to pay, you can get them back when you file a tax return at the end of the year (typically in February-April), but you are essentially giving the US government an interest-free loan.

The institution you work for should have some resources and can help you with sorting out your tax situation. Local/state laws, countries of origin, your visa type, etc. can all influence your tax situation. The information I provide here is a guideline to know what your approximate income will be to help you make decisions about housing, etc before you start a position, but you should always study or get guidance on the particulars of your tax situation to avoid needing to correct things in the future.