Yah so power supply plugs into the wall converts power from AC->DC. The power supply gives DC power out to the input power of the charger itself. The parallel board I would skip on for the time being until you have the basic charging stuff figured out. Once you have power going to the charger you should be able to select LiPo charge or LiPo Balance charge (ideally) from the list. The main battery cable and balance lead plug from the battery into the balance charger directly for now (skipping the parallel charger).
Once you have everything hooked up when you select balance charge most of the time you have to hit start to get the charger to show you how many cells it senses connected to the balance port and then you hold start to actually start charging (this interaction may vary some).
The parallel board you use if you want to hook multiple batteries to the charger but for the moment I would skip on it to avoid extra complications. You’ll want to be sure your batteries are very close to each other voltage wise before plugging into the board (looks like you grabbed the one with fuses which will help avoid accidentally rapid charging from one with more voltage to one with less voltage, you want them to be within .2-.3 V of each other overall typically if you are going to parallel charge, when you hook in parallel the batteries/cells will ‘self-balance’ with other cells they are hooked up to through the parallel board.
Only things to note are when you go to start charging you need to be sure the Amperage is set to something less than 1C for your battery (looks like 8Ah so just needs to be less than 8A) and you need to be positive the voltage/number of cells in series on the charger matches the reality. If the charger thinks it’s a 5S battery but it’s a 4S it would be pushing the voltage far too high (typically they have safeties built in to avoid letting this happen), other thing is to make sure Amperage is limited so you aren’t excessively cooking the battery while charging.