North Facing Window to Grow From

With a north facing window, you should take up painting (The shadows don't move as much.).

It is very unlikely you will be able to grow anything except mold. Lettuce, Swiss chard, and spinach don't need a lot of light, but they do require some. The rest of the vegetables require at least 6 - 8 hr. of full sunlight/day.

I presume that you are in the northern hemisphere (it matters and you are in an international group here) so berries and most vegies are out. You might grow some salad greens if the window gets light all day and the pot/tub is right in front of it. Vegetables are not good indoor plants so don't expect much.

Not much from the window alone (assuming northern hemisphere.) If you don't mind running a light 12-16 hours a day you can grow pretty much whatever you want where ever you want it (given space) but it does cost a certain amount both to set up and to run every day. Supplementing the window light will be most cost efficient (some free light is better than none) but non-window locations work, and if built nicely can become a focal point in the house - quite nice on those gray days.

In my experience you do not need "special grow lights" or some of the other stuff that's sold at outrageous prices for the purpose - plain old cool white or warm white or a mix of cool and warm white fluorescent tubes work fine. Mixing in some red-light sources to add to them helps a few things a little - the old way was to run a few incandescent bulbs as well, nowadays you might want red LEDs or the like.

Also look into community gardens or allotments - if you don't have a place to grow stuff at your house, you might be able to grow stuff outside, just not at your house.