Use client.println like below.
if (client.connect(serverName, 80)) { //starts client connection, checks for connection
Serial.println("connected");
client.println("GET /~shb/arduino.txt HTTP/1.1"); //download text
client.println("Host: web.comporium.net");
client.println("Connection: close"); //close 1.1 persistent connection
client.println(); //end of get request
}