How do antennas catch the correct radio signal in the air?
They don't. They catch all the signals that are within their operating band (which is generally much wider than a single broadcasting channel).
Then the receiver electronics that they are connected to selects an individual channel to receive, amplify, and demodulate or decode.
How does a certain antenna receive this electromagnetic field as the radio signal travels through the air?
It depends on the geometry of the antenna. An antenna made up of a long straight wire works by the electric field component of the EM wave driving conductors in the antenna back and forth. An antenna made up of a loop of wire works by the magnetic field component of the EM wave inducing an emf around the loop. Other shapes are more complicated but typically work by reflecting the EM field from a large area onto a smaller antenna that works like one of the above.
Why does that antenna receive it and not another conductor?
Other conductors can. That's why electrical engineers spend a lot of time worrying about electromagnetic compatibility and electromagnetic compliance.
Also, doesn't an electromagnetic signal get lost when it is received by other antennas before it reaches the target antenna?
Typically antennas aren't that efficient at extracting power from the EM wave. Also, even if they did completely absorb the power that reached them, the wave would refract around them after a few wavelengths and be available for a second antenna to receive.
How is the signal from an antenna directed towards the target?
This is a very complicated question, but it basically involves designing the transmitting antenna so that radiation from it interferes constructively in the direction you want to send a signal and destructively in the directions you don't want to send the signal.
How is the signal coming to the target antenna pulled towards itself by the antenna?
It isn't. The receiving antenna just receives the (usually tiny) portion of the transmitted signal that happens to reach its actual surface.