I reached Barnahowna from the south-east, from a spot marked on some maps as "Glensaul Loop Trailhead", M04117 63978 F. There is just enough space to park a car here by the hairpin bend without blocking the road or access to the dirt track.

Follow the track for about 3k, you will have great views of the Maumtrasna range in the distance and, much closer to you, a waterfall just ahead in the valley you're approaching. You're aiming for the ground above the waterfall which looks deceivingly inaccessible from here. When you reach the plateau and the track starts petering out, around M03281 66137 G, leave it and cross a boggy section to reach slightly firmer ground. From here it's a bog slog until you get to the cairn that marks the summit.

The ground was firm enough when I crossed the boggy plateau in late April but navigation might be tricky and the easiest route back is retracing your steps.

Unfortunately I couldn't check if the col at L996 670 C mentioned by simon3 can be easily crossed as it wasn't visible from where I was and I didn't fancy crossing more metres of bog to get a better view of it.

The walk took just over 4 hours at a moderate pace, 16k round trip. Linkback: https://mountainviews.ie/summit/421/comment/20519/