All of us radio guys face this problem early in our careers. As in many design assignments, I always tried to find a similar circuit successfully built by someone else at the same RF frequency to see what value of coils they would use and what wire diameter and what coil dimensions. This is a good way to get an estimate of where to start.
For example, below 10MHz, you can choose coil diameters over quite a range, whatever is practical below about 3 inches. If you choose something too small, you will end up with more turns of wire than are practical, that is, the coil becomes too long. If you choose a coil diameter that is too big, then you may find that you need very few turns, or less than one turn, to achieve the inductance needed, so in this case you must decrease the diameter of the coil.
It is best to avoid creating more than one layer of wire coil unless you are working below 1 MHz since this adds a lot of parasitic capacitance and lowers the SRF (series resonant frequency) of the coil which is bad.
The amateur radio publications including magazines and books are usually rich sources of photos showing receivers and transmitters operating at a wide variety of frequencies including 3.5, 7, 14, 21, 28, 50, 144, 430 and higher frequencies. Usually these publications have very good closeup photos of the components mounted on circuit boards, along with the necessary schematics, and it is these photos that will give you the best clues about where to start.
You must do some research beyond e-publications. I recommend also consulting books such as ARRL Radio Handbook and magazines such as QST. These are commonly available in North America.
As many will recommend, there are some basic formulas and calculator apps online that will allow you to calculate the inductance of single layer air-core coils. Use those. They usually require you to specify your choice of wire gauge (diameter), turn pitch, coil diameter and overall length. This is your starting point.
Try to use air-core whenever possible since you will usually want the best Q from your coil and air core offers this. When air-core becomes too impractical, it is time to consider adding a core. Ferrites are used to multiply the inductance of a specific number of turns, usually in the process of making a coil as small as possible. Cores of this type tend to get lossy above relatively low frequencies, like a few MHz, so such cores are not used that much for RF except when making RF chokes or broadband transformers. Chokes also may be wound on resistors. This is done to intentionally reduce the Q of the coil so that the choke doesn't introduce additional parasitic resonances.
If you really want to get into understanding coils, you can build a simple setup to measure the reactance of a coil. With the ability to measure, you can experiment with different sizes. This simple setup requires an oscillator to provide a high frequency sinusoid and some method of measuring the voltage of this sinusoid, like a scope or RF voltmeter. With these tools, you can just put your coil in series with a resistor, put a couple of MHz signal through them and measure the voltage drop across the coil. Ohm's law using the resistor value and output Z of the oscillator will tell you the coil reactance. A more sophisticated meter can also tell you the RF resistance of the coil, which then tells you the Q. The reactance and the Q are the most important things you will need to know. You can get simple hand held meters that can tell you these things.
https://www.electro-tech-online.com/custompdfs/2008/08/100-66.pdf
Unfortunately, these can cost a couple of hundred bucks, so are only for frequent users.
Another easy way to measure inductance is to use a "gate dip meter" or a home made version of one. With this device, you connect a known value of capacitor across your unknown coil to resonate it, and then couple an external oscillator to the coil using another coil and mutual inductance. When your oscillator is at the resonant frequency of your test coil+capacitor, more energy couples across and your gate dip meter senses this and shows a "dip" in the meter reading. Here is an example of a dip meter:
http://www3.sympatico.ca/richard.blackman/THE_DIPPER.html
Alternatively, here is a project for an inductance meter:
**broken link removed**
If you are working at VHF and higher frequencies, you can also buy surface mount air-core coils of many values. The manufacturers of these will specify the SRF, the DC resistance and some other useful stuff, so there is little guesswork. Here's an example of a typical surface mount inductor for UHF work.
**broken link removed**
If you study the data sheet for commercially made inductors, the series resonant frequency will tell you some things about applicability. The SRF is the point where the inductance of the coil is resonating with its own capacitance and it becomes completely useless as an inductor. In practice, you want to choose an inductor with an SRF that is much higher than the frequency you are working with so that it actually delivers the value of inductance it is advertised to have.