An oil lamp is very similar to a candle and the physics behind the both of them are the same. Be it a candle, or an oil lamp, it has a container in which you pour the oil, or in the case of a candle, this is not required. You just add the wick inside it so that it absorbs the oil and brings it above the surface of the oil. You light the wick here and the oil vaporizes.
As the oil vaporizes, due to capillary action more oil is drawn up from the container and the whole cycles keeps going until there is oil left in the container.
Making an oil lamp therefore is very easy. There are a number of ways you can do this, with the simplest being you making a hole through the cap of a small bottle inserting the wick through it, and filling the bottle with oil. The oil can be anything from cooking oil to paraffin depending on your choice.
The flame is much brighter, and if you get a little experience in managing the length of the wick, there is very little to no smoke too. Olive oil has the least amount of smoke, and has no smell whatsoever. Most cooking oils do have some smell but smoke less than paraffin.
If you want a little more fancy oil lamp all you do is substitute the bottle for a more decorative container. For example you can pour some water into a tall cut glass tumbler and top it with a couple of ounces of oil. This will give it two different colors and if you choose the right kind of oil, can look very nice. Also because oil is more viscous than water, you can put things that will float within the oil, like flower petals or even very light beads.
If you want the flame to be within the container, all you do is put the wick inside. Punching a hole through a cork to keep the wick afloat is more than enough. You don’t have to think too much about an oil lamp chimney, as the only reason for chimney is to keep the flame from gutting in the breeze. For most indoor purposes keeping the flame within the container is more than enough.
Check online, and you will get a number of ideas to make your own oil lamp, and sometimes combining a couple of different ones will give you a really nice looking lamp.