Cherry is not usually very hard to strip cleanly since it does not have large pores.

You need to decide what look you want, and how you will deal with the headboard if there is damage under the existing paint.

I've never stripped cherry but I've stripped lots of stuff with little nooks and crannies, and that detail certainly doesn't make it any easier. Sometimes, however, the trim is removable and that allows the job to be done much more cleanly. Or, you might even be able to remove the painted trim and buy the same trim new.

Brickeyee makes a good point that the first thing you need to do is decide whether you want to end up with it painted or not. If you want it painted anyway, then you can just scrape off the loose paint, sand the brushmarks and any other irregularities, and then repaint to your own specifications. You might not even need to paint the whole thing if you use as close to the same paint as you can get, which would be good around the trim since multiple coats of paint eventually reduce the profile and thus the effect of the trim.

If you definitely want it stripped, then you'll need a workspace and a bit of time, and the right tools for getting into those crevices (pointy scrapers, old toothbrushes). But I think even if you invest in those, you'll still have a great bed at a very reasonable price. I have to admit I find it unlikely you'd be able to remove every trace of black, but I think the end result would be cool, even if not totally like unfinished wood. And a coloured stain (rather than clear) would reduce the impact of any residual black colour.

If you can't really make up your mind, start by picking at it with a scraper. You'll have to do that either way. Then try stripping just one part. If it doesn't work, you can always abandon ship and paint it.

KarinL

Thank You Brickeyee and Karinl for the information. I am
wondering if the bed was poly stained in a walnut or painted a black color. Is there a way to tell the difference between a black paint or a poly stain on a piece of furniture? Does it matter? I am thinking about using poly stain in walnut, if it matches.
Maggie

If by "poly stain" you mean something like Polyshades(r), I suggest you try it on a piece of scrap first, preferably some with lots of detail. It is very difficult to get it on evenly. Personally, I don't like the stuff at all. You are much better off with separate coloring and finish coats, unless you are an accomplished sprayer.

Bobsmyuncle you just saved a lot of work. I did mean Polyshades! I don't want this piece to look worst than what I am starting with. I just don't have the experience for this work. I now know I am above my head on this one. I am going to sand the flat areas only and paint.
Any suggestion on the type of paint you would use? To match the other areas I need to stay with a glossy paint.
I have to finish the top of the headboard rail.

Solid Cherry? I have trouble with photos, but I wonder if the panels in your bed are solid cherry or cherry ply (which is actually good for such use, very dimensionally stable). You can pick at the back there to get a look. If it is ply, be careful not to over-sand since you will then have an ugly spot if you try to stain.
You may guess that cherry is a favorite wood of mine, so let me also make the case for how romantic, warm and welcoming the natural cherry color would be. You can work to strip, sand, and even if you don't get all the black off, rub the wood with boiled linseed oil (careful on rag disposal, those hazards are real) several times. If the headboard is really some nice hardwood, you will have one beautiful headboard. Get a good mattress, a bottle of Argentinean Malbec and a nice guy and take the weekend off! And cherry gets more beautiful as its red tones develop and darken with age, so plan on repeating step two for many years.

Cherrywood, How would you pick? should I remove paaint from the side of the bed? Would I see the edge of the plywood or would that be capped with another piece of plywood? The back of the headboard is unpainted and un-stained. It doesn't look like plywood because the wood is engraved a "simi circle" detail in the back. The photo makes it look like it is a series of squares, but if you look close you might be able to see the grain continues. I am only asking because you are offering a learning experience for me. If it is plywood, is touching this bed taking to a little risk or a lot risk? Would you do it, if it is plywood? Thank you so much!!!