Indoors or outdoors?
What light level (total darkness, full moon, etc?)
How far away from the camera do you want to be able to identify faces?
Do you have a computer that can be on all the time to record video? What OS?
Does the camera to be hidden?
How far from the router will it be?
How much are you willing to spend?
The cheapest, most basic way to go is something like
this, which is an OK, inexpensive camera ($110 or so.) You will probably have to leave some lights on.
This camera ($200 ish) has a day/night mode, but it still will have to be relatively bright (bright full moon).
Both cameras come with software to record video. There are better cameras, but they get expensive quickly.
A few other things...
When positioning the camera, watch out for backlight (sun rising through a window) and extremely bright / dark contrasted areas (headlights, sun reflecting off glass, etc)
It is probably not legal to record audio in your area, so if your camera has this feature you will probably want to turn it off.
If you want to record in near-total darkness without the giveaway of a red glow, look into covert IR illuminators. All IR illuminators have to be used with a camera that has a day / night mode (black and white after dark).