I will be arriving at terminal 4 (American Airlines) and 45 minutes later my friend will be arriving at terminal 1 (Delta Airlines) I would like to know where we could meet so that neither of us would have to travel too far. The meeting place should be recognizable and familiar enough that airport authorities could direct us to the spot. I have no idea how large the airport is.
There is a lot of informtion here:
http://madrid-mad.worldairportguides.com/terminal-maps.php You need to take a shuttle from T4 to the the other terminals. Your best bet would be to meet at Delta baggage claim in T1. There should be a screen that tells you which carousel your friends bags will be on.
The airport sprawls over a very large area and terminals 1 and 4 are a long shuttle ride away from each other. Here's info from the airport's site http://www.aena-aeropuertos.es/csee/Satellite/Aeropuerto-Madrid-Barajas/en/Page/1237554326802//Public-transport.html Click on the Public Transport Map.
If you are staying in the city together, it might be easier, if not as chummy, to meet at your hotel.