I've just used the example.
No. The example doesn't use mySerial and it doesn't print the value of client.read().
If you are going to modify the example, feel free to do a good job.
mySerial.print(client.read());
if fine IF you follow that with
mySerial.print(" ");
so that you see something like
webserver13 59 80 20 21 51 72 3551163616664147128352011369512340
or
webserver135 98 0 20 21 51723551163616664147128352011369512340
See, it's how the numbers break apart that is important.
I only connect the tx y rx ports to pins 2 y 3.
And ground, too?
Why aren't you using the standard USB cable to connect the Arduino to the PC?