Overclocking and heat management are the only real ways for significant performance gains beyond upgrading. Learning how to overclock can save you a significant amount of money and allow you to get the most bang for your buck. Imagine buying a i7 3820 and getting better performance than a stock i7 4770 by overclocking it. Most intel processors are not overclocking friendly though. The ones that are have a "k" on the end of the name to let people know the multiplier is unlocked which is the "easiest" way to overclock without any real trouble. Your processor is not a K variant so you would have to overclock using the FSB (frontside bus). The problem with overclocking the FSB is that it affects your ram and motherboard bridge speeds (the link between your video cards, audio cards, network cards, or even onboard stuff). in most cases large FSB overclocks require multiple voltage increases and also memory timings changes while a multiplier overclock is as simple as increasing the multiplier and voltage to the CPU usually. There are some programs that do it for you out there but these are never a good idea for cpu overclocking, it should be done through the bios manually.

Video card overclocking is also available assuming your card supports it. Some video cards are manufacture locked just like processors though. Make sure you check into it before you buy. Usually video cards come with programs that allow for overclocking much easier.

The I7 3820 is a non k variant so you would have to overclock the FSB. I looked online and it says it has 8 cores and a turbo of 3.8ghz. 8 cores is a waste really and you are not going to see a performance drop with alot of background processes or programs running with 8 cores. FFXIV will see more gains from a higher single core speed than from 8 cores. If I were to overclock your CPU, i'd literally disable 4 of the cores and get a higher/stabler FSB that way. 4 cores is more than enough for FFXIV and a few background applications. I looked online and it looks like 4.5ghz is very achievable on this processor but I wouldn't do that without a liquid cooler.

Honestly I wouldn't want to walk anyone through a FSB overclock due to damage risks. If you don't know what your doing, I don't recommend this but if you decide to try, remember to start small and ease upwards. Do not go instantly putting in large changes. You have to run a program like prime95 to check for stability, simply booting windows is not enough. Sometimes you can increase it by 1-3 without having to change anything if you were lucky and got one of the best chips on the line. Remember the FSB affects alot of things and you may have to change more than one voltage. RAM is manufactured to run at certain speeds @ certain voltages so you will have to check your rams specs.

Video card overclocking is much more easier... Heat management is as easy as drilling some holes in the side of your case and installing a push pull airflow with 2 fans bottom and top if the side panel on the case does not have fans. Still need to use a program to monitor temps though.