The way reservations at Koya-san worked when I went a few years ago was that I faxed a request to the centralized reservation office (they probably have e-mail by now). I went there upon arrival, and they gave me my temple assignment and directions on how to get there. (Contact information is given in most guidebooks.)

These are working monasteries, so it's not as if there are going to be major grades of luxuriousness, but my room was like that of a mid-level ryokan (no private bath, the only explicitly Buddhist feature being a blanket covered with sutras), and the food was vegan, but ample and delicious. You're expected to attend the 6:00AM service, and really, since it's all in classical Chinese, you just sit and listen.