That's easy. Unplug it from the wall socket, press the PSU switch to "off" and then unplug all the connectors from it. After that get a Philips headscrew to screw it out of the case and that's it.
For the CPU, you can get the above mentioned FX 8320E.
Cryorig H7 CPU cooler to keep it cool. It's a decent, cheap cooler that gets the job done. But if you want to overclock, gonna need a beefier one.
As you already have 8GB ram, you can just add another 8GB. You need 2 identical ram sticks to run in dual channel mode. These days, 16GB is a must. For your platform, AM3+ a 16GB DDR3 kit usually at 1600MHz would be good. Mixing ram is never a good thing, I'd suggest getting a new 2x8GB kit and sell your existing 8GB to someone.
For the GPU, a 1050 Ti would be great. It can run all games at 1080p anywhere from low to high, depending on game. eSports titles easily 1080p max. Ideally a 1060 6GB would be better, but GPU prices aren't the best right now.
Another option is wait for them to drop down in price or wait for new GTX series to be released. Should be soon (Pascal i.e GTX 10XX-series are 2 years old).
And for the power supply, I'd suggest a 500W and up. Corsair grey label CXM series is good, SeaSonic Focus Plus and Prime are even better. EVGA G2, G3 are also good. CXM will be cheaper though. PSU is the most important part of your pc, so cheaping out on it is never a good thing. Might as well get an excellent unit for a piece of mind.