A microphone
Something to record the microphone
Something to playback the video and original audio
Some headphones for the talent to wear while they attempt to match the original dialogue.
I use Pro Tools, but this can be accomplished on practically any multi-track audio program. Matching ambience is tricky, but the general approach is to record your ADR dry and then mix in ambience from the original scene.
On a PC I would recommend using Cubase SX3 as an audio app. You can very easily import your video file, with dialog as one audio track. You can edit that track as you see fit and can then record directly into the program as if you were in a studio. It's very powerful. You'll also need a decent audio interface, for PC I would recommend looking at the M-Audio line. For a mic, you can go a number of routes. I've always been a fan of large diaphragm condensers but a good hyper would do well. If you're trying to match audio, then use the same mic you used in the field.
This is really important advice to follow. Also, hopefully you have some "wild sound" from your location to mix with the audio that you will record in your ADR session. If not, try to go back to the same location and get some; without it, you will have a difficult time making a convincing match between your location and ADR takes.