All of the material in your soon-to-be-fire needs to be piled up in such a way so that the fire can easily move from the tinder to the kindling to the fuel. The easiest way to do that is with a ‘pyramid’ or ‘tee-pee type configuration, where the tinder is on the bottom, with a layer of kindling over it and the fuel above that.
Make sure that there is plenty of room for air to pass between the various pieces; otherwise you won’t have enough oxygen to make the fire burn. With a properly laid fire, you can strike a match or spark to the tinder and get it burning. Once the first flame starts, the rest of it should work more or less automatically, with your fire eventually lighting the fuel. Once the fuel is burning well, all you need to do is add additional fuel from time to time.
Of course, if the wood being used for the fire is damp at all, it will take much longer to burn (if it will at all). The reason why it won’t burn is that the water contained in the wood is absorbing the heat, preventing the wood from absorbing enough heat to ignite. As heat continues to be applied to the wood, the water turns to vapor, absorbing a huge quantity of heat in the process. It isn’t until this process is finished that the hydrocarbon gasses start leaving the wood so that they can then catch fire.
Basically your best bet is to make sure that you have the driest tinder, kindling, and fuel possible.