Fine views abound, but going can be wet slippery in the winter, especially the last 50m of ascent.
Easiest access is via the Kerry way from Gowlane, but it is possible to access from Peakeen West (from Molls Gap road): no real sense in approaching from N or S. The trig point stands alone atop a rocky perch and is visible from miles away. It's best to approach the final ascent from the north as there are cliffs east and very steep ground to the west.
Possibly the simplest approach is via the Kerry Way. There is parking for 2/3 cars at V917752 A. Proceed north along Kerry Way for about 1km, then turn directly west for another 800m up the steep, but quite doable eastern slope. Mostly rocks, grass and short heather underfoot. The small summit area is a rocky outcrop. About 80/90 minutes car to summit depending on conditions. Linkback: https://mountainviews.ie/summit/348/comment/5108/

For this summit, there are parking spaces for a few cars at V917 752 A, where the public road meets the start of a dirt track going Northwards. This is part of the Kerry Way and used to be the old road from Killarney to Kenmare in the 19th Century. As you pass between Peakeen and Knockanguish, stop at the highest point on the road and turn off left. Stay to the North of Peakeen to avoid the cliffs. After the ascent and as soon as the ground levels out, you will see the trig point high up on Peakeen to your left. Carry on a bit further and try and approach the summit from the North / North-West where the going is easier. The most striking thing on the summit is the trig point which is mounted on the highest rock and really stands out. Despite the fact it is just 555 metres, the views from it are stunning and are better than many other higher peaks. Return by the same route and avoid the cliffs and crags to the East. Done in conjunction with Knockanaguish, it would make for a really nice 3 hour walk on a clear sunny day. Linkback: https://mountainviews.ie/summit/348/comment/2302/

Parked in place referred to by john_desmond. From there it's a twenty minute walk up the Old Kenmare-Killarney road to the place marked on most maps as 'the Windy Gap' (though some maps like the one on this site place that nearer to Foardal, higher on the west side as one continues on that road). Then went left, but think I might have stayed too near the east side as found the going quite steep and seemed to be doing a fair bit of clambering. Took about 30-40 minutes to get to the trig point, once one leaves the road. Views from the top are stunning, down the Kenmare Bay and across to the Cahas, across the Glas Loughs to Foardal (the 'other' Windy Gap) with the Reeks behind, over to Knockrower. Going down was tricky enough, quite wet, so took it easy, but about 15-20 mins to come down. Well worth it for the scenery. Linkback: https://mountainviews.ie/summit/348/comment/3593/

From the Kerry Way at R 910 768 B to the east of Peakeen we threaded our way up through crags to gain a northern shoulder. It’s a bit of a pull, but after the exertion of Knocknaguish I was enjoying a second wind. There’s a brief scramble through more cragginess shortly before gaining the summit, a trig-pillar perched atop a rocky outcrop. Linkback: https://mountainviews.ie/summit/348/comment/2748/