I actually don't think the spatial metaphor implicit in the distinction between left and right is very helpful to anyone. It comes from where people actually literally stood relative to the king in revolutionary France. From wikipedia:
One deputy, the Baron de Gauville explained, "We began to recognize each other: those who were loyal to religion and the king took up positions to the right of the chair so as to avoid the shouts, oaths, and indecencies that enjoyed free rein in the opposing camp."
The terms have been morphing and expanding over time in some really bizzarre ways that you could spend years studying. Usually, anarchists are considered to be on 'the left,' albeit very very far to the left. This kind of makes sense at least in that anarchists tend to (arguably) be communists of some sort, but there are some very important differences between anarchists and regular communists.
As dot mentioned, there are anarchists who consider themselves to be neither left nor right. I think that this is probably the most sensible position to take, especially because it tends to confuse people. It kind of depends, though, on what kind of anarchist you are. For instance I can't see an individualist or a Tiqqunist calling themselves a leftist, but that label might make a little bit of sense for an anarcho-syndicalist.
As for liberal, that's a term that came out of the French revolution as well - it's the ideology that overthrew monarchies, basically. I consider everyone involved in state politics to be a liberal in the sense that they support liberal democratic states. Most people, though, use the term liberal to refer to e.g. members of the Democratic party, which is different. Either way, I don't think anarchists can possibly count as liberals. Some of us might count as leftists, but not liberals.