Choose the volumes of CO2 you want in your beer. Cask-Conditioned Real Ales have around 1.5 to 1.9 volumes. Most other ales and lagers have about 2.0 to 2.7 volumes. Belgian ales, German wheat beers, and sour beers typically have 2.6 to 3.0 volumes.
Select the temperature of the beer.
Read the PSI of 100% CO2 that you need to use to get that level of carbonation at that pressure.
1. For dispensing a keg of carbonated beer, I pick the volumes of CO2 I want and select the temperature at which I'll be dispensing the beer. Then I read the pressure in PSI off the intersection and set the CO2 tank regulator to that pressure.
2. For force-carbonating beer (which I can even do at a temperature different than that at which I'll be dispensing), I pick the volumes of CO2 and the CURRENT temperature of the beer, then set the CO2 regulator to the pressure off the intersection and shake the keg or bottle until I stop hearing CO2 flowing through the regulator. I can then disconnect the CO2, chill the keg or bottle to serving temperature, and I'll still have the desired volumes of CO2 in the beer. Remember to lower the pressure of the CO2 to proper pressure for the serving temperature when you reattach the CO2 to the keg.
I created this table from the formulas for CO2 solubility in average-strength beer at various temperatures. Pressures will have to be different for higher specific gravity and/or higher-alcohol beers. You can calculate these differences (https://www.researchgate.net/publication/277688911_Carbon_Dioxide_Solubility_in_Beer) or you can just experiment. Note that there will be a pressure drop for each foot of tubing (for example, 3/16-inch ID vinyl has 3 psi drop per foot), so if your line is too short for the dispense pressure, the beer will exit the faucet at great velocity with excess pressure and you'll have excessive foaming. One way to handle this is to choose the beer line length depending on the dispense pressure. So if your pressure is 15 PSI, you'll want just under 5 feet of 3/16-inch ID vinyl beer line, so you have 1 PSI at the exit of the faucet. What I do is have an adjustable pinch clamp in the beer line that allows me to adjust the pressure drop and slow the flow to have a reasonable beer velocity into the glass.