How do I learn to design a 50Ω coaxial interconnection/interface?
Have you read Wikipedia: Impedance matching and particularly the part about transmission lines ?

An example of a transmission line is the RG58 coaxial cable you mention. The confusion start with the fact that this cable is a transmission line with a characteristic impedance of 50 ohms. Yet when you measure it with your multimeter, there's no 50 ohms to be measured ! It either open (between core and shield) or a near short (couple of ohms, depending on how long the cable is) between both ends of the core and both ends of the shield. Where's that 50 ohms ???

Well, if you would like to transport signals over this cable this is where the 50 ohms comes in. Only if you apply the signal from a source with a 50 ohms source impedance and at the other end terminate the cable with 50 ohms to ground, will you be able to transfer the signal properly ! If you omit  either of the 50 ohms resistors the signal will reflect and disturb itself. The value of 50 ohms is a property of the cable, an RG 58 cable needs 50 ohms. There are also cables that need 75 ohms or 600 ohms.



Transmission lines is a subject that is not so much a part of "transistor electronics" so that's why it's not mentioned in The Art of Electronics. If you search for books on RF-design then for sure you will find books on this subject.
Note that many RF-design books are on RF-IC design, most of these do not include information on transmission lines (except for on-chip transmission lines maybe).