I just installed a new light fixture in my kitchen where an old one was. I have it all wired-up the same as the old light, but it doesn't work. Would a picture(s) of my wiring help you to see what I did wrong?
Okay ... if it doesn't work they you have to start over (obvious answer) but before you rip everything out you might want to check the bulb (it seems crazy but I've seen and even done some very forget things myself like turning on a new light with no bulb and doing the classic facepalm ... not saying you did that, just that I have before myself). If it's not a simple bulb, then did you flip a circuit breaker and before working on it and not reset the breaker?
After those two somewhat obvious tests, remove the light and see if the light is a functional light (I would rig up my own test involving alligator clamps attached to the end of a cut off old electrical cord I've made myself for testing electrical things and then plug it into an outlet (if you're not comfortable with electricity basics, like not getting yourself shocked, then please don't try what I described above ... I've been shocked a few times and over the years have a very healthy respect for the power of electricity).
After taking everything apart, test to make sure that the switch you think controls those wires actually does (yeah, I read "the old light was working part" but if the switch doesn't control the wires then you might have replaced the wrong thing ... switches go bad too and last summer I replaced a light switch that was shocking my sister in her house even after the switch tested out fine. The shock was my clue that something wasn't fine so after not finding any other problem I merely replaced the switch.
That's all I can guess for you for now with the limited information you provided. If you have access to a volt meter or other electrical testing device then your troubleshooting will be much quicker but that's kind of pricey if it's not a tool you will use very often.