Oh and I forgot to say, don't waste money on lots of string cleaning fluid (a little does help).

A scotch pad (cut off the sponge leaving a few mm to protect the fingerboard when you clean under the strings, and put a cloth under when doing the top) will restore round core strings to nearly new.

No amount of cleaning will restore hex core strings because you can't get at the six slivers of dirt inside. (Except boiling - but I'd only recommend that for bass strings, as smaller strings are too tight to let the dirt out).

Tom