Introduction to Terrans in Starcraft 2
Interested in playing as the Terran race or curious about the new updates? Here are two excellent guides that methodically take you through the new changes and abilities of the Terran buildings and demonstrate how the Terran units work. It's a bit old, but most of the information on that particular build of the game is still true.
What is good about the following videos is that they succeed in illustrating what the Terrans can do and also point out some weaknesses to be careful of. Each unit is used in a sample situation to show what the unit is good against and what can defeat it. Very entertaining videos, much better than the ones with really bad background music or self-absorbed narrators. These are not how to play videos, but they give you lots of great ideas on things you might not know your units could do. Personally, I'm going to start using Silos as blockades.
Part 2 of this demonstration:
For actual tutorial and how to information, I would recommend the official strategy guide. It's a very thorough resource with information and breakdown of each unit, abilities, upgrades, and strategies (like suggested build orders).