How does a bipolar transistor work on logical level?
I agree with Brian and Ignacio that this (an ECL exlusive-or gate) is a bit much to analyze for a beginner. 

T7 and T8 (and the associated diodes and resistors) establish bias voltages. You can assume UH1 and UH2 are constant voltages between '0' and '1'. This is one missing part to the puzzle. 

The other important thing to know is that the transistor with the higher base voltage in a differential pair will be 'on' when its base voltage is higher than the base voltage of its counterpart (assuming it's seeing some emitter current through a resistor or current sink- a resistor in this case). 

So right away we can see that only one pair of T3/T4 or T5/T6 will get emitter current, depending on whether B is higher or lower than UH2. The other pair will have no effect. 

So if B is high, then T3/T4 are active, and if A is high then T3 is on. If T3 is on, then T10 is off and Q2 is low. T4 is off and Q1 is high. 

You can figure out the other three possibilities.