From your other thread, you have a Y700 desktop?
This should be your motherboard - and the relevant places you'll be dealing with a PSU.
Then, you have a 1070?
So you have the PCIe connector at the end of the GPU. It should be either a 6pin, or an 8pin. You'd use the 6+2 from the PSU (should be labeled "PCIe") and either put the 6 and 2 pins together to form 8, or just use the 6 aspect depending on the GPU variant you have.
Then, for both your SSD and HDD you'll be switching the SATA 'power' to the new PSU.
An HDD or SSD will have two aspects to it:
The data, you won't have to touch. That's a cable running from the smaller side, to the motherboard. You don't/won't have to remove that to replace a PSU.
The power aspect, will come from the PSU - and there may be a chain of 3 or so connectors on one long cable.
You'll see it's keyed, forming an "L" on one side - that corresponds with your HDD/SDD, and will only go on one way.
The only other variable is if you have an M.2 SSD. If you do though, you do not need to provide any cables to it - it's directly mounted to the motherboard, and you don't need to worry about it here.
NOTE: The PSU you're looking at is modular, so all cables connect/disconnect on the PSU side too. There will likely be a bunch of cables you do not need. They're present to ensure compatibility with various systems, potentially multi-GPUs etc. You have pretty much the basics to worry about, and don't be concerned if you have cables left over.