How to upload program to board using Arduino sketch ver 1.6?
The checkmark button is used to compile your program (which "verifies" your code), but does not upload it to the board. The "arrow" button is used to compile and upload your program.

If you cannot connect to the device, make sure the correct COM port is selected on the Tools->Ports menu, and make sure you have the correct board selected on Tools->Board (usually an Arduino UNO).

If you have not installed the drivers yet, you will not have a port present for your Arduino. If that is the case, here is a great tutorial that will help you get everything installed and set up correctly: https://learn.adafruit.com/lesson-0-getting-started