I have a routine / ritual with my brush fires. First, I mow a low cut circle around the brush to keep the fire contained. I wait for one or two days following a decent rain. Same day should also be low wind so as not to blow embers too far. I plan to light on the side facing the oncoming wind so the wind will blow the flames into the pile. To start the fire, I take some diesel and used motor oil, mix and distribute in my intended ignition area. Let set for 5 mins to soak. Then cram a section with newspaper and twigs and then light it up. If the pile is dry enough since the rain and the wood is dried out, it should be fine. Now that said, since I personally don't like burning piles with the possibility of there being wildlife in it, my vet said the best time of the year is following the first frost. Great idea but that usually means I have to wait a while since the rain comes less frequently that time of year.
If you run into a situation where it just won't stay lit, a leaf blower can do wonders. Remember that the more oxygen you feed a fire, the hotter it gets. So, if you have trouble, Get as much wood burning as you can and use the leaf blower to crank it up.