The article is pretty vague about it, though, and only mentions the methods in a single sentence:

During the 19th century, government weather services began to record measurements more systematically. By the 1930s, observers had accumulated millions of numbers for temperatures at stations around the world. It was an endlessly challenging task to weed out the unreliable data, average the rest in clever combinations, and compare the results with other weather features such as droughts.

Adding interest to the game was a suspicion that temperatures had generally increased since the late 19th century — at least in eastern North America and western Europe, the only parts of the world where reliable measurements went back so far.

They make mention of some temperature stations and anecdotal evidence, but I still don’t know how NASA arrives at a value for average global temperature so they can plot it as a data point in their graph above.

And, as always, Drudge focuses on Truthiness rather than Truth. Yes, there are actually these titles out there (true) that make these sorts of claims (true) which are abusive and ignoring of the evidence.

Another item re the no change since 1998 claims, for example, is: New GW denialists’ deceptive lie on global temperatures.