TNT or creeper explosions will trigger TNT. I'll bet every nickel I have that Bed, Ghast, and Blaze explosions do it also, but can't test that easily right now. If you set fire to TNT or if fire spreads to TNT it will trigger it. This means lava can ignite TNT..though remember the TNT needs to have one of its six sides free so that the fire can spread to it; a TNT block entirely submerged in lava or surrounded by blocks will not ignite. If you are holding flint and steel and you punch (left click) TNT it will ignite. This is the cheapest way to ignite TNT because it will not diminish the flint and steel's durability. Redstone current will trigger TNT. The easiest way to use this is to make a lever (one cobble block, one stick, easily craftable without a table) and set it off using that.
I've tested all the above, and you can do so too easily by popping into creative mode or a test world (you can make one in creative and then swap it to survival mode with seedscope.net) Good luck!