Where to buy the bombs
Melissa sells bombs in Julienne's shop. You need its activator (explosive-activator : an arrow) as well in order to activate a bomb.
How to use the bombs
Please see the following images by clicking them.
Tips
I would like to share some information on the power of the bombs. Till your level reaches about 15, even the smallest bombs would be much effective. Probably, most enemies can not survive the explosion of the LV2 ones, and also the rest can not survive that of the LV3 ones, I suppose. I think you will never need the biggest bombs even if you are enjoying a much harder game. If the LV3 bombs were not helpful to you, please try the biggest ones.
There is one useful bomb 'Chloroform'. While the explosion of the other bombs are judged as a hostile action, that of 'Chloroform' is not. It makes targets paralyzed for a long time. I hope it will help when you play a thief character.
I have a suggestion for the times when you place a bomb. As you know, you can place your thing by holding the left button of your mouse in your inventory. However, I would recommend you to drop a bomb instead, by holding the 'Shift' key on your keyboard and clicking a bomb in your inventory, and then you can choose the number of the bombs that you are about to place.