How can I make an infinite fire?

You need to use a Netherrack block, as all other blocks burn up or won't catch on fire.

Nethererrack burns for ever.

Prior to the 1.3 patch, you could make an infinite fire by lighting a block of wood / log on fire so that only one side is burning, and it would stay infinitely burning. However, that was fixed in 1.3, so now the only way of having a block infinitely lit on fire is to get Netherrack somehow (be it buying it from an in-game shop, mining Coal Ore with a Golden Pickaxe if your server has the Golden Nether mod, or simply going to the Nether if your server supports it) and lighting it.