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I don't think it does any actual amplifying. I think it just acts as a gate and when a certain small voltage or current passes through its base, it lets the larger voltage/current input through. I forget if it's current or voltage
think of transistor as a tap. The control is base, the outlet is emitter and the water supply is the collector. Now you vary the pressure on the control knob and the water flow varies.
Now in the domain of electricity, current is the water. When you vary the pressure(electrical current) on base the current flow from Collector to Emitter changes. Also the changes on base are in terms of uA and the Collector-Emitter current varies in terms of mA or A. It is important to note that the current flowing between Collector-Emitter comes from a different source (transistor doesn't generate the charge and current), this source is Vce or the Collector-Emitter biasing power supply.
The current fed to Base comes from the signal to be amplified. This small signals give base a varying input, as a result of this the C-E current is varying. Only fact is on the base side the variations are in uA and on C-E side it's in mA or A. So what transistor is doing is, it is sensing the input signal at base and making a copy of it on the C-E side and also this copy of current is in mA or A (and this is done using a different source, the one between C and E). so the small signals on base are appearing as large on C-E side, thus it is amplifying the magnitude.|dw:1348485023876:dw|
the image got clipped, here the part on transistor side |dw:1348485494521:dw|