daughter in law pays rent to me, she now needs tenant agreement  to get benefits, how will this affect me tax wise. i'm retired in own home?

her paying you is am income and must be declared and taxed , in other words you are breaking the law , and you daughter has every right to as for a tenants agreement , after all she pays rent to you , doesnt she . You rent the property , so you must follow the laws , such as declaring the money to the irs (tax dept) and pension department and have a signed contract under state laws .

why is she living with you in the first place? 

they not married were together but broken up. She pays towards living costs not actual rent. She wants to claim rent from universal credit (UK), they want a rental agreement before they pay. She's not paying anything now, she was working but had a baby went on maternity leave and not returning to work.

In the UK you can't get benefits if you rent from family.

That aside ,having a legal tenancy agreement is safer for you (it makes her legal obligations of rent etc binding). Make sure you know what being a landlord means

In the US, no different than it did before. You were ALWAYS supposed to report the rental income on a Schedule E, and you were ALWAYS allowed to take any legitimate costs of producing that income as deductions against that income. Whether or not you would be taxed on net rental income can't be answered without detailed info from you.

If she lives with you then she won't get benefits for rent in the U.K.

As long as you are properly reporting that rent income as you are legally required to do then it does not effect you at all. 

What country?

If in the UK, family members can claim help with rent if renting from a landlord who is a family member, but they do need to provide a proper rental agreement from you.

If won't affect you tax wise, as you will already be declaring the income to the HMRC won't you. And if she lives in your home, you can rent a room out and earn up to £x a year without declaring it

UK answer: as your son's wife, she is a member of your household, not a tenant.  Money she gives you is now considered a contribution to household expenses and not taxable but her income will affect any benefits you receive.  Does your son live with you too?  Daughter in law will need to rent from a non related landlord to be able to qualify for benefits.  She cannot get her nose into two troughs at the same time. 

If UK based then you need to register with HMRC 'rent a room' which enables you to earn £7,500 annually tax free BUT not for family, same goes for her getting housing benefits it will not be paid for 'family renting' having a rental contract or not