I looked at your pics and you have a very nice backyard with nice sized pool. it will look great when sparkling clean.
Just some questions:
1. Did the previous owner leave any pool tools such as leaf net, pool brushes, or pool chemicals?
2. I see floating chlorinator in the water, find any chlorine tablets around? because of this..you will want to make sure the pool store or you (when you get your test kit) tests for CYA level and post the results along with the other pool levels.
3. Do you see where the slide gets its water from? a hose hooked to the house of from the pool pump?
4. Can you tell if there is an automatic pool cleaner in the pool anywhere? I know you cant see to the bottom but maybe some hoses floating or partially visible. look around the skimmer or the side walls of the pool.
The valve controls for your filter system are very common. I will try to explain:
The pipes in front of the pump going into the pump are the pump vacuum (supply) lines coming from the pool. Water comes from the pool to the pump through these pipes. The hand valve in front of the pump selects the source of where the water is coming from, one pipe would come from the skimmer (square opening on side of pool at waterline). The other pipe is either from your main drain at the bottom of pool or a dedicated pool cleaner line (why i was asking if you saw a pool cleaner). The valve selects one or the other or maybe both at the same time if you put the handle in the middle position.
The water goes from the pump to the filter. you have a sand filter which is common. the valve control on top of the filter selects the mode that the filter water flow is in. There should be positions for the valve called "filter" which is the normal position used when cleaning your pool and day to day use. Another position should be labeled "backwash". this reverses the flow through the sand inside the filter to clean all the dirt trapped in the sand and send the dirty water out through another pipe that I cannot see in your photos. it may be on the other side of you filter. If you see another pipe that just stops and is not capped, this is probably your waste line and is where the water would come out. Usually you connect a temporary hose to it and drain the water out to curb, but it might be plumbed all the way to your curb already..don't know as I can't see the pipe and how its finished.
There may be other positions on the filter valve such as "circulate" which bypasses the filter. "closed" closes off the input pipe to the filter and "winterize" drains the filter for winterizing the pool equipment. Only change valve positions when the pump is off. You can get the model number and manuf name of the filter and probably download the manual for it from the net.
The clean water from the filter flows out the pipes on the pool side of the filter and can go back to the pool through the two pipes shown with another valve used to select which one. One pipe should be connected to the returns ( the small openings called jets on the side walls in the pool), The other pipe might be for a fountain, dedicated pressure side pool cleaner or possible the pool slide (why I asked about that above).
Start stocking up on plain liquid bleach ( no scents or thickeners added). If you haven't already, try to get everything out of the pool such as leaves, twigs, dead animals... that you can before you start. Once you start adding bleach to start the shock process, you will want to brush and vacuum the pool daily.
If you can get estimates of pool depth and dimensions, we can calculate volume and once you have test results, we can recommend shock levels and other things to help you. You may try to get pool depth by using tape measure inserted till it hits the bottom at shallow end and deep end. or maybe your pool leaf net pole used as a measuring stick.
Welcome to TFP and we'll have you fixed up soon, but have patience. As others have already told you, the shock process can take some time and there are some strict criteria you need to pass before you are done. Read up on pool school, especially the shocking your pool section.