If i attack with a creature that has double strike, lets say its a 4/4. My opponent blocks with a 2/2.
The blocker dies during the first strike combat stage, but then does the "second strike" go on to damage my opponent? Or it just does another 4 to the already dead creature?
The second strike is implemented as an additional combat damage step in which only certain creatures assign damage. The double strike creature here is still not allowed to assign damage to the defending player because it is blocked, and does not have trample. Since it cannot assign its damage to any creatures (they're dead), it assigns no damage.
Remember that all double strike does (and all first strike does) is give a combat phase two combat damage steps rather than one, and restrict which creatures assign combat damage in those steps (C.R. 702.4b, 702.7b). Neither double strike nor first strike otherwise changes how creatures assign or deal combat damage. In particular, double strike doesn't mean—
that a creature with that ability assigns twice its power in combat damage (see also this thread), or
that that creature assigns and deals combat damage, then assigns and deals combat damage again, with nothing in between.