I've not tried growing veggies in a basement - but this link may help.
http://www.gardenguides.com/97974-grow-vegetables-basement.html

A word of caution - check your local by-laws...... http://eatdrinkbetter.com/2011/05/11/canadians-fined-5200-for-growing-veggies-in-basement/

Not Growing in a Basement/Cellar but I am currently doing massive sprouting, as I find it easier to get down there X amount of times a day, plus I am sprouting in a outside building as well but I want to see how different temps effect the process etc Micro Greens and Sprouts along with a few pots of herbs/greens that I grow are about it in the house, I like to bring in horseradish roots and nettle roots as they will both grow well over in the winter light from the window's.

Currently working on a expanding my sprouting/fodder from extra's for the chickens to being a way to reduce the feed bills for the piglets/milk cow, might not seem like garden, but its growing greens in house that in the end provide food to the family, so it kinda counts right?

Well since we live in BC, I would look to in the direction of one of our biggest horticultural crops, the weed growers.
They have been doing it in basements, in bunkers, and semi-trailers for years with a lot of success.
You might want to look at wall gardening, it offers some challenges, but keep the floor free for other growing.
Buying just a UV lamp that fits into a regular light socket could be a good way to get started small scale, while you find out what works and what doesn't.

You need a ton of light to grow most crops well. 400 watt or 1000 watt metal halide or high pressure sodium, usually a combination to get all the wavelengths. The power required will cost about $40 per month for the 400, $100 for the 1000. This is why grow ops try to steal power. I do use a 400w MH light to start seedlings and you notice it on the hydro bill.
Bottom line - it can be done but it's expensive. Sunlight is free.
Better to grow outdoors in the summer and store it by canning, freezing and dehydrating.

LED grow lights are just coming to market, maybe check those out. Prepare for sticker shock.

Look into Solar tube lighting, or the derivative of it which uses panels and a concentrator reflector with split dispersion.

You could use one of these, or a variation I guess.
http://www.aerogrow.com/

I use a 8 bulb fluorescent fixture to start seedlings in the spring but you could for sure grow whatever under it. It uses 8 X 4 foot bulbs at 40 watts each.

As an experiment last winter I set up 2 sets of 4' shop lights, side by side, each had two daylight tubes in them.
I grew lettuce under it and had more lettuce then I knew what to do with. Was feeding it to the chickens.

Also I had brought in my bell pepper plants and a couple on tomato plants all in pots. I didn't think the peppers or toms would do much, but I had peppers coming left and right on them. Enough to put some in the freezer after I used many of them.

The toms didn't do as well, as they were just about done when I brought them in. However I did get flowers and they in turn, gave me tomatoes.

As the lettuce grew I ended up buying another set of two lights and set them up on yet another stand.
This was just in a north/east facing room that was not being used so both stands were in there. So no sun really played into getting light in there.

I will be doing that again this winter too. There is nothing like pickin a fresh pepper off a plant with snow on the ground to make an omelet. Some even went in to salads from the fresh picked lettuce. 🙂

So its worth a try at it, if you feel so inclined to do so and need that gardening fix. 😉