Fire Bombs can be crafted in your Crafting Menu ("Q" as the default key to open it), but cannot be found in any chests and cannot be obtained by any creatures (currently, as of R38 in January 2017).
The crafting recipe for Fire Bombs will be unlocked by
- crafting or finding a Diamond Mining Cell that can rarely be obtained from Things, mainly as a pet-harvest
- obtaining a Warmworm Tooth from Warmworms that spawn on blocks of the Stalactite layer (like Siltstone and Stalactite) or the Lava layer (like Hardened Lava or Igneous Rock), either by killing and looting them, or by taming them and harvesting from them when they are your Pets
- and by crafting Armor-Piercing Bombs, that can also occasionally be found in Diamond Treasure Chests
To craft 4 Fire Bombs at once you'll need (as of R26 in December 2015):
- 2x Gunpowder, found in Wood Treasure Chests, or looted or pet-harvested from Hot Feet from the Lava layer
- 5 (blocks of) Hardened Lava mined from the Lava layer, which requires at least an Iron Mining Cell
- 1 Warmworm Tooth obtained from Warmworms from the Stalactite layer or Lava layer by killing or pet-harvesting from them
- 1 Shrewdshrew Tail obtained from Shrewdshrews in Savannah-biomes, either by killing and looting them, or by taming them and harvesting from them when they are your Pets
Fire Bombs can not only damage player-characters and nearly every creature (not sure about the fire-resistance of Warmworms and Hot Feet though), but they can also set all natural and artificial inflammable blocks on fire.
In cold environments, Fire Bombs will only cut a fiery hole of max. 7x7x7 into ingitible material like Tree-Leaves, Tallgrass, Shrubs, Wood, Logs, Thatched Walls, blocks of Carpets and/or many kinds of wooden crafted blocks like Wood Wall (however neither Bungalow blocks nor any kind of Roofs as of R26 in December 2015).
In hot environments, Fire Bombs can do much more damage; because once a fire is started, it is able spread to other combustible blocks and such a forest-fire could break out. Also a whole Janky House or Wooden Fort might burn down nearly completely, and there will be nothing left of any inflammable blocks, furniture or materials.
The spreading of fire can be disabled in the world options by the owner of the world (even F2P) or by claiming an area and disabling the claim option for fire spreading,
Still you should refrain from using Fire Bombs in hot environments like Savannahs, Jungles or Shores, and also be extra-careful when placing torches close to inflammable material/trees in warm to hot biomes.
Fire Bombs can melt Ice (also Ice that you might have produced yourself by throwing Freeze Bombs at Water or placing Water or Mineral Water into cold environments), and since R41 Fire Bombs can now also melt Snow.
When throwing Fire Bombs at Water (or Bog Water or Mineral Water) directly, this will make shallow bodies of water evaporate immediately, with a maximum size of 7x7 blocks in width. If there's still water left around, it will flow into this hole and fill it partly. Throwing Fire Bombs into deep waters will create a large (7x7x5) space/hole of air underwater that will quickly be filled with water from all sides again completely.
Fire Bombs can turn Igneous Rock into Hardened Lava and Hardened Lava into liquid Lava. Fire Bombs will burn Tar (highly inflammable!) to nothingness completely, but won't harm Coal Nodes - quite the contrary. Currently Fire Bombs can turn Sand into Salt as well (as of R26 in December 2015), but this could be changed again in future updates.
If you throw a Fire Bomb at flammable blocks, vaporable liquids or even Tar, but nothing starts to burn, then either the "Disable Fire Spread" option is enabled for the whole gameworld, or the "Fire Sim/Spreading Enabled" claim option is disabled for the player claim you're on, or the usage of Explosives is disabled for the Adventure that you're currently playing. Also please note that Hot Feet and Warmworms seem to be immune to Fire.
Fire Bombs can also burn away Corrupted Leaves and Corrupted Wood when thrown directly at them, as these flammable materials also make for great Fuel for your Forge. However the fire does not spread further on corrupted materials.
So the hole from one Fire Bomb won't be larger than 7x7x5 blocks, and torches or items with open fire like Campfires or Fire Pits are also not hot enough to set corrupted materials on fire. When throwing Fire Bombs at Corrupted Water, a large hole can be created in this liquid, as corrupted water is inflammable and such vaporable as well (not by torches though since their fire is not hot enough).