A good place to start is the KiCad web site, they have a brief run through of the simulator.
https://www.kicad.org/discover/spice/There are numerous books and articles on spice as well, a web search will turn them up.
For simple circuits with a handful of active and passive circuits the simulator is probably quite adequate, provided you can find models for the parts that are suitable for the kind of simulation required, there is a difference between an DC, AC, and transient response analysis that require correspondingly more complex models. Even with a small number of components simulation times can get rather long, minutes are not uncommon.
If however, the board is complex, has an analogue/digital mix, operates at high frequencies(digital logic while operating at low frequencies, may have very fast rise and fall times), has a large number of active parts, both discrete and integrated, then be prepared to tear your hair out, it is probably unrealistic to even attempt it. By breaking the circuit down into functional units it may be possible, assuming you can find models for the parts, if not then good luck!.
Errors on boards come about from conceptual problems, miss connection, wrongful interpretation of data sheets, and poor PCB layout, and in theory Spice simulation will find many of these problems, given time.
However, If your board is complex, in this case what your client is requiring is unreasonable unless they understand that they could end up paying more their simulation results than for all the work you have done on the PCB to date. The results they see on paper will not resemble the real world results since models will never be complete enough, and the PCB layout will influence results as well. Your skill as a designer of PCBs come into effect here!
If you have been in the game long enough, and your client has been happy with your previous work, try and discourage them from going down this path(a quote for the time involved may help), they actually probably don't know what they are asking for. If you were in a team, with an expert at simulation available, that may be a different story.
Just my cents worth, good luck,
cheers,
Richard