Hello and welcome to TFP!
Before I head-off to work, I'll try to get you going a bit. First thing .... you must have the right test kit. Don't fall for "free" testing at the pool store, you'll dump money there with less than favorable results. Please see the TF-100 link below in my sig. As for your pics and equipment:
PIC 1: Filter on the right with pressure gauge. We advise to clean filter when pressure increases 25% over "clean" pressure. Square item to the left appears to be a heater. Cylinder item on top of heater looks to be a chlorinator to dispense chlorine. That white box in front looks to be a controller or power panel perhaps for automatic timing and such.
PIC 2: Just another pic of the same
PIC 3: That top row of piping is going back to the pool & spa. The flat part of the handle is the closed position. In the middle means water is allowed to flow to both locations.
PIC 4: Down below you have your pump. The pipes going to the pump are from your pool & spa with a valve to adjust suction from either location. That clear lid on the pump is to your strainer basket to catch debris that gets past your poolside skimmer. It needs to be emptied once in a while with pump "off". There should ALWAYS be water running through there to keep pump cool. Too many air bubbles can be a symptom of something wrong. That valve to the top right adjusts water going back to the pool or something else - either a water feature or pressure side port for cleaning.
PIC 5: Closer shot of what appears to be an automated chlorinator.
If I missed something, someone else will correct me.
Make sure to get that test kit and read the Pool School page for an understanding of what pool chemistry is all about. (Link below) The other links in my sig are important to you on an almost daily basis, so save them to your desktop as well.
Lastly, please add your pool info to your signature by going to the top of the TFP web page (just under the Pool School button) and select "SETTINGS". On the next page look to the left for a menu bar that says, “MY SETTINGS” and go to "EDIT SIGNATURE" to enter your pool and equipment info there. It will help us later. This link may also help you:
Pool School - Read This BEFORE You Post. Welcome!