Popular YouTube channel The Wood Whisperer demonstrates a simple four-step process for creating mortises with a router. The process, known as LTBD (Layout, Tools, Balance, Direction) is described below.
Without proper layout, you won't know where the mortise is supposed to go and you won't be able to set up your router properly. So I always fully layout one of each size mortise I need in my projects. If there's more than one of a particular mortise, I only lay out start and stop lines since my edge guide holds the router a specific distance in from the edge.
I recommend a decent plunge router, an edge guide, and a nice sharp up-spiral bit. Here's the bit I used in this demo: http://amzn.to/2rlQTMp
Unfortunately, not every router manufacturer makes an edge guide, but common brands like Bosch, DeWalt, Festool, and Porter Cable have them available. There are also after-market edge-guides available like this one from Milescraft: http://amzn.to/2sy8Yeq
The narrower the workpiece, the more difficult it will be to balance the router. So it's a good idea to double up or even triple up on your workpieces to provide extra base support. I often offset the support piece so it not only prevents the router from tipping side to side, but also provides additional support front to back (especially hand for mortises that are near the end of a workpiece).
Although mortise routing involves surrounding the bit with wood, you should still pay attention to your router direction. I recommend pushing the router away from you moving left to right. This keeps the router moving against the rotation of the bit and should yield a better cut, as the router tends to pull into the work keeping the fence tight against the workpiece
If you follow LTBD, there will be very few workpieces you can't safely and accurately route a mortise into. Get some practice with this technique and before you know it, you'll be mortising everything!