Find a point of interest

Land a ship inside a point of interest's circle of ground and it is yours. Take its survey contract first and you are shown where it is and paid for both.

You need this whenever you are flying somewhere a point of interest sits, or want a reason to fly somewhere new.

You are playing in the shared world. Nothing is found in sandbox.
To take a survey, a ship of yours has already landed on that world after a launch; until then the board deals none for it. Landing inside a point needs no survey at all. See Points of interest.
For a point that counts when landed, your ship can come down whole: a parachute on Earth, legs and engines on the Moon.

Steps

Accept its survey, if you want to be shown the way. You can skip this step and land inside the point anyway; it is found all the same, but nothing marks where it is and only the point pays. On the Administration's board, surveys are the offers whose title starts Survey: and name the point. A helium-3 deposit's survey starts Prospect: instead. Accept the one you want; see Accept a contract. If it is not on the board yet, wait for the next draw.
Check what counts. Look the point up in the list of points of interest: note its radius, and whether it counts when landed or when flying low — and if flying low, the height limit.
Launch a fresh rocket. A survey, like every contract, is met only by a ship that left the pad after you signed it. An older ship that lands in the point still finds it, but the survey then ends with its advance handed back.
Find it on the map. Tap MAP in flight and zoom in on the world. The point you are surveying is the amber diamond on the world's edge.
Amber diamonds are points you have not found; a found one turns green.
Fly there. Aim your flight so it comes down, or passes low, where the diamond is. Tap FLIGHT to go back to the ship.
Come in and look for the mast. Near the ground the point stands on the terrain as a mast with a pennant, with a post at each edge of its radius. A point the size of a building has only the posts.
Land inside the posts, or pass between them low enough. Passing low counts only under a contract that sends you there; landing always counts. For a flying-low point, keep the altimeter's AGL figure under the height limit while you are between the posts.

What you should see

A POINT OF INTEREST banner with the point's name and what it paid, a CONTRACT COMPLETE banner for the survey if one sent you, and the mast's pennant turns green. On the map its diamond is green from then on.

A rocket standing on a hillside beside a thin mast with a green pennant, under a POINT OF INTEREST banner. — Found: the pennant is green.

Note

A helium-3 deposit on the Moon is found this way too, and then it can be mined: its diamond turns mint instead of green and prints the field's grade. See Mine helium-3.

If it didn't work

There is no diamond on the map. No survey for that point is under way. Accept it at the Administration first, or land where you think it is; if its world's surveys never appear on the board, land a ship on that world.
Found it, but the survey did not pay. The ship left the pad before you signed, so the survey ended with its advance handed back. The board in flight says signed after this ship left the pad under such a contract.
Landed right beside it and nothing happened. You came to rest outside the radius; the posts mark the edge. Take off and set down again between them.
Flew straight over it and nothing happened. No contract was sending you there, the point counts only when landed, or you were higher above the ground than its limit. Land inside it instead.
In sandbox. Points of interest are found only in the shared world. See Switch to sandbox.