Services like Google Reader report their subscriber numbers in the user agent string to FeedBurner and these are then included into the total. The remainder is worked out from IP accesses, user agents, etc. It's not precise, but in terms of the relationship between one feed and another, quite reliable.
There have been ways to "game" the figures here and there (such as the Netvibes trick that went around a few months ago) but these are usually picked up and solve and reputable content providers were not using them in the first place.
A lot of people believe in numbers from places like Alexa or Compete and they're far more shady than FeedBurner's numbers. My own analysis has shown the numbers to be "reasonably" accurate, based over my own cumulative 30,000 or so subscribers on a few different feeds.
This article is rather loaded though:
Subscriber count chicklets: Nobody believes them. Nobody cares.
Since when? They're very useful, particularly to advertisers judging a market.
There are other ways to measure your RSS reach.
Like?
Feed flares: Most of these are useless junk.
When they work, they're pretty useful. I've had a lot of success with people coming in from RSS readers to comment on the site when they see other people have commented via the Feed Flare. Same for people adding to del.icio.us. Desktop feed readers don't have "add to delicious" buttons.
I do agree with the general sentiment of the piece though.