I advice you to look at Strobist: http://strobist.blogspot.com/2006/03/lighting-101.html

That site describes on very detailed manner and starting from basics what equipment you need to add light to your images and how to operate them, basing on assumption you need to be able to move the equipment with you, ie. you don't have dedicated studio.

The basic set recommended there is relatively inexpensive and extremely portable, basically one flash, folding stand and umbrella for it and way to trigger it off camera, but it already gets you very far.

If your camera is not able to trigger external flash by any means, or you want studio-like environment but cheaper, try looking at this. The writer is a professional product photographer and in that article he describes how to create studio-light-like results with $50 light set.

Also, if your camera does not have hotshoe, it's worth checking if you could trigger external flash by optical triggering, ie. tune the integrated flash of your camera low enough to not be major part of the image and then use external flash that triggers when it sees another flash go off.

This tuning can be something as archaic as just taping the in-built flash with translucent material, or taping a "light guide" next to the in-built flash, so that the flash is visible to the slave speedlight, but not to the subject. Better manual flashes allow you to turn the flash head almost 360 degrees, so you can aim the light sensor right towards the camera and still select the direction of the illumination freely.