We grow our own hay for sheep, but it's a bit rich for horses. The only fertiliser it gets is from animal droppings. If you use an artificial fertiliser you will get a softer crop, which appears to grow lush and tall, but promptly lodges (falls flat) in the first heavy rain of summer.
To harvest hay, do it ideally when the seed heads are well formed for some protein content. Just when depends on where you live, but sometime in early summer. If you leave it too long it will just be dead grass. The weather is the main factor in achieving a good hay crop. Depending on where you live you need about 5 days of sunshine and a light breeze, plus another day for it to cool down after baling and before stacking.
For the actual making and harvesting you will need a tractor, a mower, a turner of some type such as a hayzip or haybob, a baler, a trailer to cart it, plus a team to do the work and somewhere to store it. An alternative is to use a contractor to do the work, or perhaps a local farmer who makes his own hay will do it for you, in return for half the crop. If you go down the route of someone else cropping it, you have to wait your turn so losing the whole field to bad weather becomes an increased risk.
A final option if you have an acre or less is to scythe it, turn it by pitchfork then cart and stack it. To use it, you need a hay knife to slice the stack up.
Updated to add: growing hay, as with so many farming matters, is an all-year-round job. Once it's cut and cleared, young sheep go onto the aftermath, keep it trimmed and tillered, and add their dung. Over the winter, make sure there are only a few animals on so the ground doesn't get poached and turned into a muddy morass. Weeds need to be kept down - nettles will respond to frequent cutting with a lawn mower and removal of the clippings to the compost heap (it looks funny but it works); thistles need to be eliminated - the best time to dig spear thistles (we do ours by hand) is just as the flower stalk is put up, so they have expended their energy making the flower and shouldn't grow back. If you just snap them off they will grow back sixfold - dig them out root and all, then back fill the hole. Creeping thistle can be controlled by mowing as with nettles, or both can sometimes be eradicated by the sheep close grazing the pasture, especially primitive sheep. Wild flower type weeds are to be encouraged so there is a varied sward, full of nutrients and trace elements to make a top quality hay. Don't let brambles, cleavers, burrs and so on get a look in, and be vigilant to remove every single ragwort plant and destroy it. Sheep can eat a small amount of the first year rosettes, but too much, and the flower stalks are poisonous to many types of livestock.