Small charcoal grill - raise fire grill?
The issue of raising or lowering the fire is effectively a question about how to raise or lower the amount of heat that's getting to the food.

For the type of grill that you've mentioned, the typical procedure is to put the coals on one side of the grill -- either in a pile, or as a sort of crescent shape along the edge of the grill.

If you want to cook over a cooler fire, you move the food further away from the coals.  If you want to cook with a hotter fire, you move them directly on top of the coals (which can also cause flare-ups, leading to even faster cooking).

You can also put the lid on the grill and change the temperature by opening or closing the little vents on the top &amp; bottom of the grill, which will control how much oxygen is available to feed the fire ... but I've never really gotten the hang of that one, myself.