Nothing is more iconic in the gaming world than the original NES. Set it next to a PS4 or Xbox1 and it will tell them "NEAL BEFORE ME!" Ok maybe not but they definitely have a cool factor about them and are quite spacious when gutted;)
What you need is
Hot glue gun
Soldering iron
Dremmel
Mini ATX board of your choice and hard drive/DVD drive, this can be done a few ways so before you even get to step one do some research and decide what's best for you. Others use a laptop HD/disc drive for slimness I went with a desktop 500gb HD and remote USB DVD drive. Either way you'll love it.

Step 1: Gut the NES

For all the purists out there the board from my NES was later put in a case I picked up with a bad board, another NES SAVED, circle of life, blah blah blah. Ok..this is a pre-game bit system so get your Phillips and gut that sucker! Mark the posts needed to attach the to halves minus the front it must go for space. Get dremmel and CUT! Save the posts you cut you will want them to fabricate mounting points for the new mother board

Step 2: Test Fit All Components

This is the fun part! Take your components and test fit. You'll want to squeeze a fan or 2 in there and be sure there is proper air flow

Step 3: Boot It Up

I did this out of the case. I temporarily ran a SATA DVD drive to boot windows and now that it's up and going I have a remote USB DVD drive if needed...have yet to need it. You will probably have to skip to step 4 to do this as you'll need a power button to turn it on.
Pictured is the board I used, was a good find and came with a power cord with DC converter(no power supply in case, more space saved!) 4gbs RAM and built in wi-fi! That's the antenna on the back if you were wondering.

Step 4: Using Factory Power and Reset Switches

Simply solder pc connectors on the wires from the NES switches and LED power light then plug onto the board. There is a clip that must be removed on the power switch so it doesn't lock down when pressed, take apart and you'll see it. When done the power and reset switches will both act the same.

Step 5: Assemble

You know you have a working tiny pc now so put it in the case. Mine is possibly one of the least hacked up ones made but I opted for the remote DVD to do so. This is the custom part and your know-how and creativity will come into play here. I took very little off the bottom case. Sure nobody will see it but me...and you lol...but I'm happy with it.

Step 6: Play!

Sorry I couldn't be more detailed, I built this months ago and just got a instructable account. There are more out there and they are all custom, take what you can from what I did and good luck !