As Dirk said, Konjunktiv 1 is used for indirect speech. But there is an exception: That is, in quite a lot situations, Konjunktiv 1 is identical with Indikativ, and in these cases it is correct to use Konjunktiv 2.
Examples:
"Er sagte, er hat geschlafen." (This is Indikativ, therefore wrong.)
"Er sagte, er habe geschlafen." (This is Konjunktiv 1 and correct.)
"Er sagte, er hätte geschlafen." (This is Konjunktiv 2, therefore wrong.)
"Er sagte, ich habe geschlafen." (This is Konjunktiv 1, but undistinguishable from Indikativ, therefore wrong.)
"Er sagte, ich hätte geschlafen." (Konjunktiv 2, in this case correct.)
But don't worry too much, most Germans do this wrong.