As far as I understand it's supposed to go criss cross by layers with an air gap between bales for airflow. Like rotating = signs. I also like to put the cut side facing outside of the stack and not inside, but that may just be me. That could be totally irrelevant or wrong.
Technically hay should be stacked on the "cut side" down... so the strings are not on the top where you grab it. but on the side. For the first layer. So I have been told since I was a kid by every person that we ever got hay from for my horse and for eveyone I ever helped up north. Down here... not so much. And we do not put any space inbetween bales. They are packed as tight as we can get them in the loft. If there is a fire, hay that is stacked with air will create a hotter fire than hay that is packed tight as that will smolder first. But again.... if it is properly dried... that is not a problem. The biggest problem in the east is getting hay made when it is humid.... that will cause more problems than anything else. That is why I have been so thrilled with the last 2 windows for hay making late this fall.... clear, dry weather, no humidity. The fog in the mornings burns off but the grasses "expire" and the moisture is drawn out of the hay with the lack of humidity. That is why hay made out west is so superior in quality. They irrigate, get it grown well, and then have all that dry weather to get it cut, dried and baled. They don't lose the color which adds to the nutritional level too... it doesn't bleach out because it doesn't have to lay for days in a hot sun but with high moisture.
We pack ours close when we stack, mostly because it used to be a space issue. Jan's right about the aridity out west here. Sometimes we get a rainy summer which must make the hay farmers sleepless, but usually we are dry from June to late September. Very low humidity. I'm pretty sure only the alfalfa is irrigated. There is alfalfa, oat, barley, timothy . brome, orchard and mixed grasses available.
I had my hay delivered and stacked this year which was a treat. Dh is allergic and it makes him miserable. The guys that delivered alternated direction every two rows. And they did place the cut ends up on the bottom row.
I get 40-50 square bales for those times when my hay guy can't get a round bale delivered. We buy the hay, since we don't have a tractor big enough to handle a round bale, he brings it to us as needed. Sometimes, things happen, like all the tractors being out in the field, he goes on vacation or this year, he had Covid. So I fill in with square bales. I stack them tight, alternating which way they lay, just as described above. As the stack goes higher, I build steps to lug the bales higher.
We don't always get the most consistent sized bales, so we have learned to "mix and match" with the varying lengths. Not that they are that much difference, but some just pack tighter... it is also dependent on the type hay that is baled...First cutting hay will bale more consistently than 2nd cutting orchard grass. Stiffer stems will pack in a sq baler better.... Lots of little things that the average person has no clue about. And I am not saying that to be a smart a$$... people just don't know these things.... If the hay is good and dry, then stack the best way that you can get them stuffed in there. No one is grading you on the stacking job !!