1) In your client folder, for me: C:/Program Files/League of Legends, then the /Game/ folder, find HeroPak_client.zip and extract it to a separate folder (name doesn't matter). Now open that folder, go to /DATA/Characters/ and look the character you like, in my case Anivia; which is called Cryophoenix.
2) I openend it, then you see a couple of files. I want the skin of she having battle armor on, which is called anivia_battlearmor. Now I copy the anivia_battlearmor.sco, .skl, .skn, .wgt and .dds files (5 in total).
3) Now comes the important part. Go back to your client folder (/Game), open the /DATA/ folder, create a map called 'Characters', in there create a map called 'Cryophoenix' (in my case), then paste all the 5 files, and rename them all to what Anivia's original skin is called; Cryophoenix.sco, Cryophoenix.dds, etc.
4) Done!
Basically the client will read this folder first before taking the files from the heropak. Good luck.