I took apart my 3DS recently, but it was for a shell swap (The old one was peeling off flecks of blue). Regardless, a screen will require most of the same steps, the ribbon cable for the screen is embedded onto screen block itself.
For buying a screen, you can either get one wholesale from Ebay or a Part Seller, or you can buy a broken 3DS for parts, and take the screen from there. Maybe you'll get lucky and the screen will be an IPS. A quick browse of the prices tell me that getting a screen wholesale will be cheaper, but you may luck out. Who knows?
If you don't have experience or confidence in taking apart small fiddly pieces, I would steer far away from taking apart the 3DS yourself. You don't need any tools aside from a small Phillips Screwdriver to get it apart, but Spudgers help with getting a lot of the ribbon cables out, as well as opening the Low Insertion Force locks.
If you're going to go ahead with it, I put some info below, from my experience of taking apart 3DS systems.
Make sure you group all your screws as you go. If you place screws in the wrong screw holes, and screw them too deep, they can deform the plastic on the other side. This is particularly true of the screws surrounding the buttons, as screwing them too deep causes little bumps to appear.
I would say to go very carefully and very slowly. The New 3DS XL Shell Housing Replacement video by 'The Fix' on Youtube was very helpful in seeing how the 3DS is taken apart, and put back together (I am still quite a new user, so I am unable to link it directly). Ifxit has some pictures on replacement, but I found the video to be better quality instructions. Be particularly careful with pulling ribbon cables out of the main motherboard, some of the slots are Zero Insertion Force, and some are Low Insertion Force.
Also be weary of the speaker cables. I managed to break the cable while trying to take one of the speakers out, the soldering job is not the strongest. If you have skills in soldering you can fix it yourself, but it's better to just not break it in the first place.
Finally, trying to get the ribbon cables for the top screen portion of the 3DS plugged in and out of the main motherboard is an absolute nightmare. This is something you'll need to do, possibly multiple times if they weren't plugged in correctly (I'm speaking from experience on this).
Those are things I could think of off the top of my head, I'm sure there's other things to take into account when performing a repair of this type. If that all seems feasible to you, then go for it. Otherwise, you're as well off to give someone some money to repair it instead.
Regardless, best of luck in your 3DS fixing endeavor.