How do I know if I'm able to use LPV minimums on a GPS approach?
There are many websites / blog pages that compare and contrast the different approaches. All you need to do is google a bit.

That said, if your plane can fly LPV approaches you'd know that. It requires WAAS-quality GPS receiver, and to install that requires at least a logbook entry.

Note that it's not only a matter of equipment. Even when the plane is equipped to fly LPV approaches, there can be certain conditions when you can't use LPV minimums (satellites, etc.) If you CAN use LPV minimums, the GPS unit MUST show you "LPV" in the annunciator window. It's possible that you're LPV-equipped, but your annunciator window shows you only "LNAV", for example.

So, check your documents, talk to your mechanic, you wouldn't really NOT know if your plane was ever upgraded for LPV approaches. If it's your own, you'd know and have discussed it and most likely given the mechanic the task to upgrade it. If it's a rental, or you're just buying it, look at the logs and ask the seller. And keep in mind, the annunciator window will show you the lowest GPS approach type that it senses is safe. Usually on an LPV-equipped plane that will be "LPV", but it's entirely possible it will only show "LNAV", or something else. For you to use LPV minimums also depends on the actual flight condition.