My wife is a teacher and will receive a pension when she retires. How will this effect her Social Security?

The amount of retirement income you receive from other sources does not change the amount of social security your are eligible to receive.  Your other retirement income may impact how much of your social security benefits are taxable, but will not change your benefit levels.

One note about teachers.  Some school districts opt out of social security.  If this is the case for your wife, then her social security benefits may be much lower because her time and income working for the school district will not be used to determine her benefits.  The easiest way to tell if her school district opted out is to look at her pay stub and see if there is a deduction for social security.