Public telephones in Madrid Barajas airport?

Send the hotel email or call and ask them- normally they have a particular pick up point and come with a sign on the side of the bus- you shouldn't have to call them when arriving. So just send an email, telling them what termimal you are arrivng at (T4, T2 etc) asking when and where to meet you (and anyone else going to that hotel at that time). There are public phone boothes around that you can use, with euro coins. But normally all the hotels have a regular running shuttle between the airport and hotels.