How do I collect from an Anomaly tile?

From Meedoc, one of the game designers:

The anomaly reinforces the FIDS brought by the tile when exploited. To benefit from the bonus, you need to exploit it by building the city next (or above) to it, or expand and try to reach it by building a borough.

Basically it just boosts the normal FIDS yield of the tile it's on - it's not actually a special resource like Glassteel or Emeralds that you have to build an extractor on - it's just a tile that gives more FIDS than normal.

So to extract it, just get a city/borough tile next to it, or on top of it. Reaching out with boroughs to access one of these tiles usually requires getting a bunch of population in your city, and thus a long amount of play time.

The notable thing with anomalies is:

• They tend to give a lot more FIDS than normal - sometimes an even spread of food/dust/industry, but other times just a ton of, say, food.
• They sometimes give 10, or even 20 approval in the specific city that is harvesting them - approval is rare and precious.
• There are special quest-events, buildings, and hero abilities that amplify them. Ardent Mage heroes can mine an extra ~9 or so science from them, and Roving Clans heroes can do the same with Dust. The Cryogenic Monitors can add +15 science (but just in one city). There's also a trait for custom factions - Landscapist that gives them a small amount of extra yields.