Build credit for wife ?

Just add her to all or any your accounts. That said, credit without income doesn't mean much. Just being a licensed user apparently builds her credit. (Way back once I got a mastercard for my cat so i'm wondering if she has credit?) She doesn't sign her name well and can't hold a pen.

She's not ever going to have as high a score as you'd like because she isn't a separate customer and making her own payments. Get her a card in her own name, monitor her payment history, make sure she is making payments on time and for more than the minimums every month, or pay off the balance each month. The only way someone builds credit in their own name is by having credit in their own name. 

Add her name to your credit cards.

Credit is personal to you. You can't build her credit for her. It's up to each person to build their own good or bad credit.

That said, joint credit cards or joint loans might help. But given she has no income it's doubtful she will qualify for any form of credit.

by buying stuff with a credit card and making payments

Just add her to all your accounts.  That said, credit without income does not mean much. Just being an authorized user apparently builds her credit. (Way back when I got a credit card for my cat so I wonder if she has credit?)  She does not sign her name well and can't hold a pen.

Having a job is big part of building credit, and also buying things and paying things on time give you good credit. 

You cannot actually do the building.  However, you can help her by giving her money to use in building it.

If she has no credit at all, then her first step would be applying only one time for only one secured credit card.  You would give her the money for the security deposit.  If she is denied, it is never important that she stop immediately.  Continuing to apply makes things worse.  A denial or rejection does not mean to try elsewhere.  It means to stop and not try again, anywhere, for over a year.