How do you install field fence corner posts?

it depends on the type of fence, how big it is, the ground where it must be installed and many other things. It also depends on how you mean the word “hard.” It can be— invariably in my experience— grindingly hard work, especially in a Texas summer. But it isn’t a major building challenge. Assuming your fence is not masonry or a rock wall:

1. Locate the fence line. I usually use a string and stakes for this.
2. Determine where the posts have to go. You need one everywhere the fence makes a change in direction, plus one on each side of every gate or other gap in the fence, plus enough in the middle of the fence line to carry the span of whatever stringers you intend to use. The span will be determined by the weight of the fence materials, the ultimate strength of the fence (are you trying to keep toddlers in the sandbox, or are you trying to keep a stud horse away from the mares in the next pasture?), the materials you intend and their conveniently available lengths, and other considerations. Be careful counting your posts before ordering; it’s very easy to come up short. In fact, it’s so easy this has entered the language as a meme, called “fencepost error,” a topic I suggest you search for and understand before buying your material. Having determined where the posts go, drive a stake or otherwise mark the locations.
3. Set the posts. They can be driven in the ground, or you can dig and set them in dirt or concrete. Coming from the Texas Gulf Coast, where materials exposed to the corrosive atmosphere don’t last long, I would build a wooden fence by setting Schedule 40 galvanized pipe in concrete as the posts, then through-bolt 2x4 deadwood to each side to carry the stringers. That way, when the wood rotted off the posts, I could just build a new interior fence section and bolt it between the posts. You probably don’t have to go that far. However you decide to set your posts, set the corners, any direction changes, and the gate posts first, then top them to height. Once this is done, you can pull a string line to set all the others and the fence will be straight and of even height.
4. Set the fence stringers on the posts. For a wood fence this will require a 2x4 top and bottom, minimum. For a chain link wire fence you’ll need a pipe top rail, but the bottom is usually just a wire. A really tall one— say, 8′ wire— will need a center pipe as well.
5. Then, finally, install the fence fabric.
6. Gates are another matter. Definitely use a diagonal corner brace from (upper) the hinge side to the (lower) swing side, especially if you’re building a wooden fence. Wood gates just love to sag, then they won’t close at all, or bind in place. You may want an X-brace instead of a diagonal. For long gates, I use exterior grade plywood stiffeners in the corners and at any vertical members in the center. Even then, sometimes I have to pull a cable to the top outside corner to keep it from sagging.
7. A heavy gate is hard on your hinge post. Consider, if necessary, setting an additional post 3–4 feet away and backbracing the hinge post to it to lower the stress on the individual member. Ever seen the H-shaped double post with wire cross bracing set in a barbed-wire fence, upon which is hung a metal gate? That’s how you keep the hinge post from sagging. You may also want outriggers perpendicular to the hinge post if your gate is very heavy.