Some soldering experience is assumed. This isn't a soldering tutorial. Work carefully. Assume everything inside is fragile and breaks easily. You should have received a board, flex cable, USB cable, and tri-wing screwdriver. You'll also need a small Phillips screwdriver (#00), Dremel (with small cutting bit), soldering iron, and solder. Tweezers, and x-acto knife for cleanup are also recommended.
Remove the battery cover, battery, and all 7 screws from the back case. Lift off the case, remove the top screw from the stylus holder.
Cut away the case, making a hole for the USB connector. The capture board should be able to lie flat against the stylus holder.
Disconnect cables from the DS mainboard. The wider LCD cables are held in place with a locking mechanism. Flip up the black tab on the connector before pulling cables out. The small thin cables also have a locking piece that slides out horizontally. Remove the 4 screws from the DS mainboard. Detach the antenna wire (flick it up with a fingernail, it should come off easily). Remove shoulder buttons (be careful that springs don't pop off). Lift the mainboard out and flip it over.
Line up the flex cable with points on the mainboard. Tape it down to hold it in place. Solder the exposed pads to the mainboard. Fold over the tail end and solder it to the points labeled LDG3, LDG5.
Put the mainboard back in. Reconnect all 4 cables, locking them into place. ⚠ Make sure they're straight and fully inserted. The dark stiffener part of the cable should line up with white lines on mainboard. Reattach the antenna wire.
Remove the tape backing on the capture board. Stick the board to the metal shield, lining it up with the lower left corner. ⚠ If you make a mistake, don't pull up on the board, it's thin and can break easily. Slide a knife or something under it and pry it up. Insert the flex cable into the capture board. Flip the black locking tab on the connector down. Put shoulder buttons back in, being careful not to pinch the flex cable under the shoulder button. Screw down the mainboard and back cover. Put the battery and battery cover back in.
TROUBLESHOOTING: If the DS won't stay on (it powers on briefly and pops off), check that the cables are completely inserted. In particular, the top LCD and backlight cables can cause this. If the DS doesn't turn on at all, check that the battery terminals aren't bent / stuck / obstructed. If there's a problem with the captured image (colors look wrong or display stays white), it's probably a soldering issue. Hit F12 to open a debug window. Look for "STUCK" messages to show which points may not be soldered down. More problems? If you didn't like these instructions, let me know how I can make them better.