We still need to know your precise power supply. Would you mind opening your computer case, and taking photos of your power supply, which should show the brand and model #? While you're at it, it would also be helpful if you took a few additional photos of the inside of your entire build. Then upload the photos to imgur and post the link here.
Question: What exactly are you trying to accomplish with this upgrade? For example: Are you trying to play the new Doom at 1080p at 144 FPS? What exactly is your goal? Why the upgrade? Sounds like a great idea and I applaud it, but I just want to make sure you'll achieve your goal. Also, I strongly suggest that you create a parts list or build list on PCpartpicker.com, so that you have an precise idea of what's in your current computer, and also have a plan on what you're upgrading to.
It would be helpful to have a budget, but if you don't have one... I suppose you can answer the questions I stated above and then I and the others can respond with upgrade advice, along with what it will cost financially to achieve it. Please don't forget to state your monitor resolution (or model #) and the power supply question is even more important.
Motherboard: H81M-S1 (revision not specified)
http://www.gigabyte.com/products/product-page.aspx?pid=4669#ov
Storage: 390.6 GB and 540.9 GB: 1 TB hard drive formats to 931 GB, which is the approximate total of your two drives. Based on this fact and their odd capacities, I'm sure that you have a 1 TB HDD that has two logical partitions.