You must use general knowledge from understanding circuit design. In fact the exact make and model of capacitor or resistor are very rarely critical to the proper operation of the circuit.
For example, in the case of C1201, you probably would NOT want to use a capacitor of significantly LOWER value than is shown because that will reduce the ability of the circuit to smooth whatever ripple there may be on the incoming source. And if you used a capacitor significantly larger than the specified value, you may risk of a current surge during power-up cycle.
And you certainly want to select a capacitor (in any part of the circuit) that has sufficient voltage rating for that point in the circuit. For C1201, for example, if you know FOR SURE that the incoming "+5V" is already regulated or otherwise reliable stable, you might get away with a 6.3V rated capacitor. But you may want a higher voltage rating if the source is the very common raw output of a mains-supplied transformer, rectifier, capacitor arrangement. Or some other source with a wider range of expected voltages.
C1203 may be more critical as it provides some stability for U1200. Recommend studying the MIC29302 data sheet to learn about the special role of the input (C1202) and output (C1203) capacitors in voltage regulator chips.
Bypass capacitors like C500 and C501 are added as needed ("season to taste") to maintain quiet power into chips like U500. Bypass filtering is partly an "art" and sometimes a pragmatic exercise of trial and error.
With rare exceptions, the exact KIND of capacitor is not a critical factor. A chip ceramic or SMD electrolytic or even tantalum would likely be equally effective, so it is a matter for the product/board designer to select the proper component that meets not only the requirements of the electronic circuit, but also the space available on the board and the budget for the project, etc.