Let me preface by saying I know very little about computers. Not much further than a basic understanding. But I'm trying to upgrade certain parts of my sort of crappy computer (PSU, graphic card, and RAM) for my kids. How can I tell what is compatible with my computer? Thanks so much.
Graphics cards - the main thing to check is the power supply. It needs to be powerful enough for the system, and provide whatever power connectors it requires (6-pin and/or 8-pin PCI-Express power connectors).
The memory, well, google your motherboard and check the manufacturers specifications. They'll also have a QVL list, which lists memory kits they've actually tested and confirmed. But other memory of the same type should work fine in general, at least as long as you don't mix and match different memory (that CAN work, but the risk of problems is certainly higher).