I'm starting with internet connection because it's absolutely free to use locally and can also be used to communicate abroad with no charge. The best and most well known program to this end is Skype. It's completely free to sign up and make video calls with anyone, anywhere in the world (as long as they have Skype too!) I recommend this to travelers and expats alike, as it will save you a boatload of money.
Where Can You Find Wifi?
Many pubs and cafes in Edinburgh also offer free unlimited wifi connection. Here are the locations that I recommend.
In the Old Town:
Cafe Nero: 1 Parliament Square (on the Royal Mile next to St. Giles' Cathedral)
Starbucks: 124 High Street (on the Royal Mile)
Cafe Musa: North Bank Street (the Mound)
Lovecrumbs: 155 West Port
Brew Lab: 6-8 South College Street
Hula Juice Bar: 103-105 West Bow
In the New Town:
Fredericks Coffee House: 30 Frederick Street
McDonalds: 3-9 St. Andrew Street
Cafe Nero: 15 Multrees Walk