There are three separate sources of free Public WiFi access.
The Main one is via an ariel from a resident halfway up the hill overlooking Arillas, who beams it into town.
Depending where you are, this will determine your access, so check for wireless networks and log on.
As Zoe say's two good locations, also opposite the Condor, and in Aquarios when sitting at a table nearer to the Athina Hotel.
The Condor supplies a strong WiFi signal, when inside the Condor.
There are also private networks, who will let you log on, Bar38 has done this for a couple of years now,
but you have to ask for a key, they don't charge if you buy drinks.
San Stefanos Travel has a private network for a fee.
The WWW Bar has WiFi and a few others that you need to do a search for first.
There are some dead spots in the village and you won't get any signal.
I heard that Teresa's may be doing WiFi as well. Delfino has a private network.