To answer this question, I'd first have to know what kind of fireplace you have. The easy way to go about that is to look in the access area down under the window of the fireplace. Down near the valve, you should find a metal tag, which will have a manufacturer name and a model number on it. Type those into Google, for example "Heat N Glo 6000TV Manual" to find the manual, which will have complete and specific lighting instructions for you. But what if you can't find that? Well, let's go over some general procedures for various appliances.
If you can't find a metal tag in the fireplace, there's a good chance you're using a gas log set, which is a burner dropped into a pre-existing wood burning fireplace. There are several ways these can be lit. If you don't see any kind of control mechanisms at all, you've got a match light burner. You should find a metal flange with a square hole in it somewhere near the fireplace. This is the gas valve. If you don't have a key, purchase a "universal gas key" from a local hardware store or online. Get a long barbecue lighter and place it over the burner. Then and only then, turn the key counter-clockwise to start the gas flowing. Just that simple, away it will go.
There may also be a safety pilot kit on there, in which case you'll see a knob on one side or the other, and there will also be a little pilot assembly attached to the burner. These work a lot like an old water heater. You find the pilot setting on the knob, then push it in (if you're not sure, just move it until it pushes in). Then you'll use the same barbecue lighter to light the pilot. Hold that knob in for 20 seconds or so until the sensor on the pilot heats up, then let it out. When you want the burner on, turn the knob to on. Then go back to pilot, on, pilot, on, etc. When the season ends, or you go on vacation, turn it off entirely.
If you don't see that knob, you probably have electronic ignition. For these, you should see a switch that says off, remote, on. That switch box will almost certainly contain batteries. Start with replacing those batteries, usually AA but sometimes 9V. At that point you can just use the manual switch to get the flame lit. If you don't hear a beep when you push the button on the remote, you may have to re-sync. There will be a button near that switch that will say reset, sync, or something along those lines. Push it, and you should hear a series of beeps, then push the power button on the remote, and you should again hear a series of beeps. Now be patient, the startup cycle can take up to 45 seconds. Once you hear the beep, just wait. You'll hear some clicking and clunking, and eventually the fireplace will light. If it hasn't been used in a while, you may have to go through several cycles to bleed out the air and get gas flowing again.
That's it for the log sets, let's move on to fireplaces and stoves. Many but not all of your newer appliances will be electronic ignition. For those, really all you should have to do is push the button on the remote or wall switch. The most common reasons nothing is happening are that the batteries in the remote control are dead, which is an easy fix, or that the remote is out of sync with the receiver. Follow the same process I described above for electronic ignition log sets to get that back in sync. If you hear a beep and clicks, but nothing happens, you may just need service. There really isn't much outside of changing batteries and syncing the remote that the average homeowner can do to fix these. There are some fireplaces that will lock out the control module if you push the button too many times, or if the fireplace just won't light for a variety of reasons. It may be necessary to find the control module of the fireplace, and get to the reset button there. The control module is generally a black box,roughly the size of a few cell phones stacked up on top of each other.
A lot of the fireplaces that were built before sometime in the mid 2000s used a millivolt ignition, which is similar to the safety pilot process I described for the gas log sets. You'll need to open the access door, or on a freestanding stove you should find the valve down on the bottom of the stove. Then you'll see that knob on the valve that says off, pilot, on. You'll set it in the pilot position and push it in. Then there will be a button with a spark or lightning looking symbol on it. You'll click that until you see the pilot flame ignite. Hold that button in for about 20 seconds, when you let it go the pilot should stay lit. Now turn the knob to the on position. From there there's typically a wall switch that you need to turn on to get the fireplace going.
Beyond that, I'm sure you already know my advice: Call in to your local dealer. If you can't get your fireplace going, chances are it hasn't gone in quite a while, and could use a good cleaning and service. The technician will be happy to show you exactly how to get it burning, so you can have a nice cozy evening.