This is what we're starting with:
Before getting started with the full project, I sanded and tested a single coat application on a piece of railing that's not visible from the ground floor. I wanted to check on how "light" a sanding would suffice, and I wanted to monitor drying time. That's pretty important since we have a lot of traffic going up and down those stairs on any given day.
I broke out 220 grit sandpaper and sanded the railing so that the topcoat of the current poly was roughed up (it no longer had a shine to it). Using painter's tape, I taped off the tops of each spindle where it met with the rail since we're leaving those white. Then, using a short handled 2" brush, I lightly applied one single coat. It's important to keep a steady hand, going slowly with the grain of the wood. You can see from the image below that 2-3 coats will be needed to achieve the desired depth of color, but it worked well!