The Make 1 Right increase is the most widely used M1 increase. It has a slight right slant and is easy to use.
This is what it looks like before you make the increase. You're going to insert your right needle under the running yarn (indicated with the arrow) from front to back and place it on your left needle:
It will now look like this:
Treat this loop like a normal stitch and knit like you normally would.
You'll see a slight hole (as indicated by the arrow):
But not to worry! Just finish your row in pattern and it will be ok. See, no holes!
Ta Da! You've completed a M1R.