It is possible but I will allow others to give their input on that topic.

For all of the readers that do not have a place to garden check with your city, parks department esp, or garden clubs to see if your area has community garden spots. Many cities have set aside vacant land as community garden areas. Most you would pay a small rent or volunteer to help in the garden area. If your city does not have one see if the city would be agreeable to starting one. Some cities/counties have small parcels of land that are too small to build on but can be used for this purpose.

Good luck. In a couple of months you too could be growing in soil. Check your produce section of the supermarket for fresh herbs.

Do you have a bright window where you could place a couple of 4- to 6-inch pots? Window gardening can be tricky--too much sun, refracted light, indoor temperature--but it is not impossible. Why don't you choose two or three herbs that you use often and then go by the garden center and get a 2- or 3-inch start of each and grow on. The investment would be minimal and you would quickly learn if you have an indoor green thumb. Try to keep the soil moist, but not wet. Turn the plants daily. Pinch the amount you need for fresh seasoning.

Here is a link that might be useful: HarvestToTable.com

Traditional grow lights are expensive and not really suited to apartments. It is possible to get a grow bulb that will fit in a normal lamp: http://www.homeharvest.com/spotgrowlightbulbs.htm is an example. Now, I ordered something like this online, spending $20 - $30, only to discover my local garden store carried the same kind of thing for $4. Shop around.

You can buy an electrical outlet timer for less than $5 at a larger hardware store. That way you don't have to worry about accidentally baking or starving your herbs.

I haven't tried the glass bulb self watering thing.

You'll still have to put your herbs where the cat can't reach. I know, easier said than done.

Growlights as 4 foot long flourescent tubes in a shop light fixture, costs about $4-5 for each 4 foot bulb and about $12 for the light fixture, sold at Home Depot. These cover a wider area compared to the round bulbs and reflectors. To get the best lighting the link below has one that can be up to 2 feet from the plants. Avoid those glass watering globes. They are not very well suited to seed starting.

Here is a link that might be useful: Charleys greenhouse

FYI on the glass watering bulb. It only works on plants that like moist soil. When the soil starts to dry the water is releast. There for if you have a plant that likes to dry out between waterings or likes a barely moist soil the watering bulb will give too much water and likely will cause your roots to rot.

Are window boxes a possibility? They can be fun, pretty, and productive! Check out the article below for some ideas...

FataMorgana

Here is a link that might be useful: Apartment Living Gardening Article

Check with your apartment super if there is a small place were you could grow some herbs. In an area with lots of sun. Herbs dont need good soil. Not too much water either. Imagine you will start something good going......?
ladybug6a

You could try an aerogarden herb grower. It uses hydroponics, and requires little maintenance. My friend uses one for strictly growing basil. He loves making homemade pesto.