First, you'll need to cut a piece of the acrylic rod down to size. I cut it slightly longer than the total width of my blank, so that I could have roughly a 1/8" overlap on either side.
To get a good adhesion of the glue to the acrylic rod's surface, you'll want to scuff up the length of the rod using a piece of coarse grit sandpaper. Then, you should deposit a line of wood glue on the acrylic rod.
As you insert the acrylic rod into your wood blank, you'll want to spin the acrylic to cover both of the surfaces with glue. Because I counted on a press fit, I had to use a mallet to get the rod fully into the blank.
Wait for the blank to dry before doing any more work with the blank - very important. I'd give it a day to cure, or else you might get surprised on the lathe later.