You don't, I had this happen 6 weeks ago and you are screwed.
The HDD of each PS3 is encrypted and only works with that PS3.
If you get your HDD out and switch it to a new PS3 the first thing the new PS3 will do is reformat the HDD...
What I ended up doing is buying a SLIM and getting my PS3 repaired ( for 50$ in 2 days by a local guy), so now I have 2 working PS3 lol.........( and I did move all my saves to the SLIM once the old PS3 was fixed, in case it broke out again soon afterward). So basically I had the YLOD PS3 repaired just so I could get the data out ( I don't trust it won't break again at some point).