I know of two very popular solutions: plunge router and Drill Press.

The plunge router is an excellent solution, and there are many YouTube demonstrations of freehand and template-/jig-base methods: Marc Spagnuolo (The Wood Whisperer) has an excellent free video on mortising techniques.

The drill press is a relatively hassle-free, low-tech approach; but does require chisels to square-up corners.

The Tenons are where most people get lost – at least that’s what I’ve surmised from reading. It takes a bit of practice, but the TS and router table, used in conjunction with each other, can make short-work of ‘floating’ Tenons. I make my own Domino Tenons, and have it down to a simple process. If you’re interested, please let me know.
MJCD