How do web browsers find out the MAC address?
So, how does the computer find out the MAC address of the server?


It doesn't. The MAC address only has validity inside a local area network (LAN), which, as the name says, is local. Unless the destination IP address resides in the same network as your machine, what it does is create a packet destined to the target IP address and forward it to its default route, usually your router. (To do so it must obtain the router's MAC address too using ARP—but this is a different matter.) Obtaining the server's MAC address is the task of the final hop which is in the same LAN as the server; a machine notices it is the final hop by checking if the destination IP lies in the same subnet as its own.

It is only when the destination IP is in the same local network as your machine that the MAC address needs to be obtained. (And this is done using ARP too.) In this case, your computer just happens to be the final hop in the route to the server.