You need to take a crash course in alliances -- there are 3 major ones (Star Alliance, Skyteam, and OneWorld).
Star Alliance currently includes United, Air Canada, and US Airways (for the time being)
Skyteam includes Delta and Air France/KLM (+Korean)
OneWorld includes American and British Airways (+Cathay)
In addition, Alaska Airlines is a "free agent" of sorts that partners individually with many airlines, most of which are in Skyteam/OneWorld (but Alaska isn't in either alliance, it partners individually with many of those alliances' airlines).
When flying airlines, you should be consolidating an alliance's flights to one partner program. Keep in mind that some partners don't always offer miles for certain fares on their partner airlines, so you have to make sure of that when you purchase tickets.