If I am in a domestic partnership and my partner only uses school benefits? How do I claim them? I am paying for his tuition because I get the benefit through my work.

If your domestic partner qualifies as your dependent, you can claim his education expenses. Otherwise, you cannot.

He qualifies as your dependent if he passes ALL the following tests:

1. The person can't be your qualifying child or the qualifying child of any other taxpayer. 
2. The person must live with you all year as a member of your household (and your relationship must not violate local laws). 
3. The person's gross income for the year must be less than $4,050. 
4. You must provide more than half of the person's total support for the year.
5. The person is a U.S. citizen, U.S. resident alien, U.S. national.
6. The person is not a married person who files a joint return unless that joint return is filed only to claim a refund of withheld income tax or estimated tax paid.

If he is not your dependent, your partner is allowed to claim the tuition credit on his tax return, even though you (or your employer's plan) paid for it*.

If your employer imputed income to you, on your W-2, for the benefit, you (or your partner) have paid tuition with after tax money.

*However, if the benefit was a pre tax benefit, it is treated like a tax free scholarship, and you (or your partner) cannot claim the tuition credit. 

But, you can elect to report some of the benefit  as income   and then claim the tuition credit. For example the American Opportunity Credit only requires $4000 of tuition for the maximum ($2500) credit. You would only need to report $4000 of income.