For example this is the rate 1/2 coder. We see that, for every information bit that comes in, the two code bits go out and the way they go out is the following. You see you have got the first bit with present bit gets added to past to past bit for C(1) and for C(2), you get the present bit past bit and past to past bit did not get added and get to give you the value of C(2).
One could very easily see that the value of C(1) and C(2), get generated by a generator polynomial, which is, in this particular case, G1 equals to 1 plus D squared and G2, equals to 1 plus D plus D squared.