Good Luck, these are not real easy but not too bad once you get past the spring.
There is a flat coil of spring steel inside the cord head (usually on the back of the spool) and when the pull cord snaps this spring steel comes unwound as well. The only way to return it to normal is to rewind the spring steel before replacing the cord.
First, remove the cord head (the same as when you originally replaced the cord) and remove the new cord.
Then rotate the cord spool counter clockwise and see if there is any tension on it. If there is then leave some tension on it and rewind the string (keeping the tension on the spool).
On the ones I have done there are little metal tabs holding the spool in place, simply bend these up and you will be able to hold some tension on the spool while winding the cord around it.
If there is no tension on the spool or if you hear a rattling sound then your spring may have come off or broken. Just remove the spool and replace the spring (available from most lawn & garden stores, but probably not WalMart). Then wind up the spring until there is some slight tension on it and wind the cord as mentioned above.
It is also possible to leave the retaining clips holding the spool in place, wind the spool up as tight as you can against the spring, insert the cord and let the spring tension wind the cord around the spool as it normally would. Any time I have tried this I have not gotten the spring tight enough so the cord does not fully retract onto the spool, I have always had to pull the spool, tighten the spring, then wind the cord manually, YMMV.
If, after the whole thing is back together, the cord still does not retract far enough, remove the cord head again, unbend the retaining clips and tighten up the spring some more.
Be carefull, a flat piece of spring steel under tension with sharp edges can be dangerous to work with.