Good questions.
First thing, if you don't have an aftermarket cooler you should never overclock. People may do it and not have any problems, but it's not a safe idea.
Stock cooler:
Aftermarket:
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
Aftermarket coolers have better heatsinks and fans for better cooling.
There are a few programs that you may be able to use based on your motherboard. However, the traditional way to overclock is through the motherboard BIOS. There are two ways to really overclock, change the Front Side Bus (FSB) or the Multiplier. You should read a few overclocking guides before you overclock your CPU to understand the process. Don't worry if you have a different motherboard than the one in the guide. Read to understand the concept and process.
http://www.tomshardware.com/forum/263043-29-1156-core-core-overclocking-guide
http://www.overclock.net/t/605848/i5-i7-lga-1156-overclocking-guide-to-4ghz
There are a few programs you can use to monitor your system and get information about your system. I personally like RealTemp and CPU-Z. You can get information about your system with CPUz (motherboard, RAM etc)
http://www.techpowerup.com/realtemp/
http://www.cpuid.com/softwares/cpu-z.html
I doubt you would need a new power supply. The one you have powering the 6950 should be adequate for a new GPU.