Keep hands away from your autographed guitar. Touching or brushing against the autograph in any way affects the longevity of the ink in a couple of ways. The oil from your hands, though it may not seem like much to you, deteriorates ink over time. As the oil breaks down the chemicals in the ink, your autograph will fade. Besides oil, the physical act of touching the autograph creates enough friction to remove a small amount of ink. If you or someone else touches the ink over a number of years, there may be nothing left of the autograph.
Apply a small amount of hair spray or nitrocellulose lacquer to the autograph to preserve its longevity. Test this application on another guitar or surface with similar characteristics as your autographed guitar by writing on it with pen and spraying the mark. If the test does not make the ink run, proceed to spray the autograph. The spray will seal the ink to the paint of the guitar, safeguarding against normal environmental factors that affect signatures.
Keep the guitar in a dry room that does not receive a lot of sunlight. Humidity will not only cause the guitar to swell up, but will also break down the ink of the signature with the addition of moisture. Sun will also fade the ink of your guitar over time until it is barely legible.
Display the guitar in an area of your home or gallery that does not receive a lot of traffic. People spell disaster when it comes to collectibles. Admiring eyes can easily turn into grabby, ruinous hands. If you want to sell the guitar at a later date, and do not care about displaying it, store the instrument in a safe, dry place.