The first step to getting your guitar back into shape is to remove the old, dead strings. This will allow access to the fretboard and headstock so they can be more thoroughly cleaned.

Do not remove all 6 strings at once, as this would suddenly and drastically alter the tension on the neck, which could lead to warping. If the neck becomes warped, new strings that are applied may end up too close or too far away from the fretboard, causing either fret buzz or strings that are difficult to press down. Instead, remove the first 3.

Using your string winder, begin to unwind the smallest (high E) string with a string winder. When it is quite slack - plucking it no longer sounds like a note - pull out the pin where the string enters the bridge on the body.

Carefully pull the string out of the bridge pin hole, then unwrap the string from around the tuning peg. This should not require any cutting. Be careful not to scratch the headstock with the end of the string!

Repeat this for each of the next two smallest strings (the B and G).