Well, um, it's basically just understanding the components of matter, breaking them down, and reassembling them into a new form. We use transmutation circles to circulate the alchemic energy and to specify what it is we're trying to do. Like this...
[The alchemy talk has pepped him up a bit, and he pauses from the weeding to draw a circle in the dirt.]
For example, this circle would make certain weeds in this plot wither and die, so it would be easier to pull them out.