What exactly do you mean by the term "figure out"?
All you really would ever want to know about a p.s. is:
1.) It's max power rating, e.g. 300 Watts, 400 W, etc.
2.) It's intended mother board(s) format, e.g. ATX, BTX, whatever,
to ensure it has the proper connectors.
3.) How many auxiliary device power connectors it has, e.g. how many drives of all types can it connect power to? And if there's connectors for the newer SATA drives that might be in system. They use new standard connections, incompatible with all older standard designs.
How to determine these without internal inspection.
If it's a preconfigured name brand system, then they probably have a Web site, with Tech Support pages, perhaps a keyword search engine, and you can lookup your model number to get the detail specs, which ought to include p.s. max power rating, perhaps mobo type which will tell you what connectors are on the ends of the p.s. output wires. It may also tell you the p.s. model #, manufacturer brand, etc. These details can inform a system upgrader or modder, what's compatible with the p.s. for projects e.g. adding additional drives, RAM, a more powerful video card (some top end screamers require aux. power connection on the vid card, in addition to the bus supplies), what mobo replacements will fit and work with the existing p.s., etc.
Other than the Web site, you can call their tech support by phone, give them the system's ID info and they can look it up and inform you,
or some provide online live tech support chat pages, during certain times, where you can do 2-way Q&A chat or troubleshooting.
If tech references can't tell you the format style of the mobo, but just the make & model #, then you can go to those Web sites, enter the specific model #, and it should identify which of the common formats it is, e.g. AT, ATX, BTX, etc. which will designate what class of p.s. it is hooked up with.