I'm sorry, but when dealing with A/C systems, I'm in the camp that if you have to ask, you probably shouldn't be doing it.
Your lack of knowledge is further exemplified by you asking about the coolant filter and changing it, as the coolant filter would very likely not cause a lack of A/C, as the two systems are largely unrelated.
I get the mindset of saving money by doing things yourself, but just last week an individual stopped by the shop with an A/C complaint. They purchased a commonly available r134a gauge/can combo kit, and tried adding refrigerant to no avail. They then noticed the gauge was in the red, and proceeded to vent all of their refrigerant to the atmosphere to "get the gauge back green". Some troubleshooting by me showed the clutch relay had failed, making the compressor inop. Unfortunately for them, the system used R1234yf, and their can of r134a/stop leak contaminated the system. A system flush, vacuum and fill with the correct refrigerant had them running again, but at the cost of a several hundred dollars, instead of the 20 or so for a new relay.
Yeah, if you really have no base knowledge of refrigeration or the carnot cycle, you shouldn't mess with it.