Through thousands of km of undersea fiber optic cables. In 2014 there were already 885139 km of submarine cable. Enough to round the Earth 22 times.
Huge Brocade MLX routers, Cisco and others. with connections 10Gb, 40Gb and 100Gb with hundreds of fiber optic links connected to them. There are days when these systems manage about 4 terabits / second.
Physical diagram of AMS-IX. One of the Internet interconnection centers that are in Amsterdam. Through which, Each time you use Internet, your information circulates more often than you think over there. Each square is one of these giant routers.