What's the best way to up res images in Photoshop?

If you have CC, the new upscaling works best.  As mentioned by Mike, it and the other 3rd party plugins aren't going to be the magical fix, but the new upscale is an improvement over the older resampling methods.

Bicubic smoother is the best for most enlargements.

Don't get your hope up that 3rd part software like extensis pixel smart scale and genuine fractals. They really don't do anything you cannot do in Photoshop, and hence do not have before & after samples printed on their box. You are welcome to try them but go with the free trial if they still have. Alien skin Blow Up 3  http://www.alienskin.com/blowup/ I have not tried, but their before/after samples show a visible small improvement, which is realistic to the limitations of rezing up images. But again I do not like the false marketing promises of crystal clear images, which is not true.