I have a couple of other tips for starting coals as well that I will add in here since I don't think they warrant their own instructables.
There's plenty more info in the steps, but the take home message is shown in the video below.
Step 1: Use a Chimney
Weber charges way too much for their chimney so I decided to make my own for free using some found hardware cloth and some metal wire I had lying around.
To make the chimney, I cut up a piece of hardware cloth and rolled it into a cylinder. I then used some metal wire to sew it shut. I only had to loop through every 5 holes or so in the hardware cloth.
The hardware cloth works pretty well as a chimney for two reasons. 1) It is full of holes so it allows air to flow freely through it, and 2) it doesn't require you to pick up the whole chimney of hot coals and flip them over onto your grill risking a possible burn or fire from a wayward hot coal. Instead, when it's time to dump the coals, you simply pick up the wire tube and the coals fall down onto the grill below.
Step 2: Build and Ignite the Tower
First, I crumple up some newspaper paper and shove it down to the bottom of my chimney. I try not to use magazines or glossy paper as they don't burn completely.
Then, I pour in a whole bunch of coals on top of that. I have started using the real wood charcoal chunks, rather than the "Kingsford" style briquets. I think they burn hotter and taste a bit better. Mmm. Eat coal.
Once the tower is built, I light the paper from the bottom and watch as the heat and fire ignites the coals above the crumpled paper.
Step 3: Grab a Hair Dryer, Aim, and Blow
Find a hair dryer and take it out to your BBQ. Make note of what direction the wind is blowing and head upwind of the BBQ. Point the dryer at the coals and turn it on. Watch out for all the sparks that will start to shoot out of your hot coals.
Within just a few seconds the coals that are lit at the bottom will start to come alive and light all of the rest of the coals in the chimney.
This method has worked for me every time and you should be able to revive just about any struggling BBQ fire with this method (assuming something is still burning). I learned how to do this from a man named Mario who owns a sheep farm in Italy. Thanks Mario!
Step 4: But What If I Don't Have a Hair Dryer?
The fire is fueled by oxygen, so if it's having trouble burning, you probably want to try and get it as much air as possible. Blowing on the fire is fine, but you'll find that you will be out of breath pretty quickly and you won't have helped revive your fire too much. You can get a much more powerful jet of air by directing it through your fingers.
Take your pointer fingers and your thumbs and squeeze them all together so that you create a small diamond shaped gap in between your fingers. Take a deep breath at this point. Then, take your fingers in this position and raise them to your mouth making a tight seal around your lips. Finally, blow all of the air out of your lungs forcing it through that little hole.
You'll notice that when you could only blow for a few seconds before, you will now be able to blow air on the fire for much longer and with greater control and force. The coals should flare red and respond quickly to your oxygen infusion. Keep blowing until the coals are revived remembering to take breaks so that you don't pass out. (This works best if you can get a friend to help blow on the fire as well).
Step 5: Dump the Coals, Start Grilling, and Feast
Once the grill is ready to go all you need to do is throw on your food, cook it, and enjoy.