auch = too, also Peter bought a new car. Mary also bought a new car = Maria hat sich auch ein neues Auto gekauft. noch = still John's car is old, but it still works fine = Das Auto von Johannes ist alt, aber es funktioniert noch gut. doch = used for emphasis when the statement is in contrast to the perceived situation: You wanted to buy a new car, didn't you? (though you didn't do it yet) = Du wolltest doch ein neues Auto kaufen, oder? For the position, the same rules as for "nicht" apply: Even though each of these words is an adverb, you preferably put it in front of a suitable object in the sentence, which is then modified by it. If that is not possible because it would change the intended meaning, you put in front of the verb. In a main clause, one cannot put it in front of the verb, so in that case (which doesn't happen too often) it goes to the very end.