Experts will tell you that giving a full critique is difficult from photos, and they would be right as you can't see how the horse moves or if their stance in one particular photo is the way they normally stand or if it just happened to be a picture taken at a wonky moment.
However, proper pictures maximize the odds of being able to give/receive the best critique possible online.
If you are going to ask for members here to take the time to type out a detailed and proper critique, the least you can do is take the time to take proper photos.
1) The horse doesn't have to be super clean, they don't need a bath beforehand, but it does make it easier to see the underlying structure of the horse if they aren't caked with mud.
Horses in summer coats are ideal, but I know they aren't always possible. Keep in mind when you ask for a critique that a thick winter coat can sometimes change the way a horse looks.
2) The horse needs to be standing on flat, level ground. If the ground isn't level, then it can make the horse appear to be much more downhill/uphill than they truly are, and un-level ground can also make the angles of their legs, shoulders, and hips seem different than they truly are...therefore, making proper critique impossible.
Grass footing doesn't make for good critique because it can hide their hooves and their pasterns, depending on how tall the grass is. If you have access to a paved road or a concrete slab, those are the best places to have conformation photos taken as you can see the full horse down to how their hooves are trimmed, but a flat/hard dirt or gravel driveway will work as well.
3) The horse needs to be mostly squared up. Exact halter horse stance isn't necessary because horses very seldom stand like that naturally, but they shouldn't be stretched out with their front or hind legs way out from underneath them (unless that is the stance their breed standards call for). They also shouldn't be all crouched up with their legs perched way up underneath them like they were standing on a pedestal.
If your horse stands in either of these ways normally and it is not their breed standard, then there is likely something going on with their health that should be addressed by a vet.
4) The horse needs to have their head up at a level that they normally hold it at and it needs to be pointing straight ahead. While some horses will stand nice and calm with the proper position on their own, most people find it easier to either have the horse tied or have another person holding them. If the horse has their head turned toward/away from the camera or if their head is down and they are eating, that makes critique impossible because you can't see the whole horse.
5) There should be no less than 4 pictures taken. One straight from each side, one straight from the front, and one straight from the back. The photos from the sides should be of the horse's full body. Do not cut off their head/neck or upper body and just post a picture of their legs. Do not cut off their legs and just post a picture of their body. A proper critique must be given by looking at the whole horse. The photos from the front/back to not have to include the whole body, but they do need to have the entire length of the legs/feet and as much of the hip/shoulder as you can get in the picture (it's usually easier to get full photos from the back than the front)
The best way to get accurate photos without distortion from the angle is to stand even with the approximate middle of the horse. Look at them from the tip of their nose to the point of their hip, choose the midpoint between the two (usually somewhere around where the girth would go), and stand there, facing the side of the horse. Then, either squat down or raise your camera to get it about even with the horse's vertical mid-line (about halfway up their body). That will give you the most accurate depiction of what the horse really looks like.
Photos taken from odd angles can often make a horse's faults seem less or more obvious than they would be given a square photo.
From the front and rear, it is better if you can squat down and get just above the level of the horse's knees/hocks. That way, the picture is showing the legs straight from the front/back instead of from a downward angle, which can hide or exacerbate the appearance of faults.
Often, when taking photos of the horse's hind legs from the rear, you should tie the tail up so that it is out of the way. That way, there is a clear, unobstructed view of the horse's hind legs.
6) Make sure to include the horse's approximate age and breed (if known) in the initial information of the first post. Different breeds have different standards in regards to ideal conformation. So, it would be unfair and likely be a mediocre critique for someone like me, who's main experience is limited to the stock horse breeds, to critique a gaited horse. While there are some faults that are faults universally through all breeds, what is a fault in stock horses is sometimes the ideal in a gaited horse.
The horse's age plays a big part in the critique as well. Very young horses are notoriously difficult to give a good critique on because they can go through some very fugly stages. Even the best conformed horse in the world no doubt went through some ugly stages before they were 2 years old.
7) Consider the time of day that the pictures are taken. Around noon makes it difficult because that's when the shadows directly under the horse are at their darkest and they can obstruct the view of the horse's legs. Also, always make sure that the sun is behind you as you take the photos. Everyone knows that photos very seldom turn out well if you take them facing the sun. I prefer mid-afternoon or mid-morning because the horse's shadow is no longer directly under them and I don't have to worry about my shadow obstructing the view of the horse either.
Anyway, I think that's everything, but if I've forgotten something, then by all means remind me.
And, just because I know some folks find examples easier, I've included some of my own pictures that would be appropriate for a decent online critique.
If anyone who is not well versed in critiquing wants to try their hand at her, there are plenty of faults to pick out. Keep in mind, though, that she is only a yearling of grade/inbred stock horse breeding.