(Oh, so close!)
"もう" and ”もっと” are used a bit differently... Like in most cases ”もう” is used to express exasperation of some action. Almost like the equivalent of "OMG" in "OMG, can we get this project over with!?" or for example, もう、疲れた！(I'm SO tired...)... Although, in the example I used above to say you were so close, I was emphasizing how close you were by adding もう. So もう can be used to add emphasis to some things as well. It really varies per the context, but in most situations its going to be exasperation.
In the example: もう早く運転してください！
If I were to translate that in English as is, I'd probably write it as (Drive faster damnit!) although if I were translating to a more G rated scene (Hurry up and drive faster!) or something. Overall if you said this to a taxi driver or something they'd think you were extremely impatient or something... or so I think.
However, もっと would work in this situation. もっと早く運転してください！ would be a bit softer than the previous example and would give a taxi driver the impression your in a hurry but they probably wouldn't think you're an impatient person or something. もっと almost always will mean "More of X"... if you want more rice when someone is filling your rice bowl you could say もっと and they'd give you more, but if you said もう they'd probably give you less rice as it would seem as though you are tired of eating rice.
That's not to mention the particle "も", もう and も are actually two different things (just to make it harder for you :P). も is used to say something is as much as something else or that something is true for something else and etc. like 私も means "me too" but 私もう really makes no sense to me atleast... Another example is like lets say you dislike homework 私が宿題あまり好きじゃないんです。 your friend could say 皆も if "everyone" does too or if its only you and 3 other people then they could say Aさんも、Bさんも、Cさんも宿題あまり好きじゃないんです。 "A-san, B-san, C-san, [and you] all don't really like homework"...
So if we were to shorten this all up,
in MOST cases:
もっと = more
もう = statement of exasperation
も = also
hope I helped...