You don't have to read music to play an instrument, but why not leverage off of hundreds of years of musical experience that has been captured through written music?

Western music is based on an octave. There are 8 notes or steps in the diagram below to get from low E to high E. For simplicity's sake, this is a C scale which has no sharps or flats. 

The notes

Here is another way of looking at it. The diagram below shows the notes of the scale in both clefs and the notes of the open strings on four instruments I play.

How can I apply this to the guitar? 

The open string notes (at the nut), with standard tuning,  are EADGBE. 

Practice this scale. Learn the names of the notes. A run from low C to high C is a C scale. 

The notes on a Bass Guitar are the top four (deepest) strings of a six string guitar, but an octave lower.

How do I apply this to the Mandolin? 

The open strings are GDAE. Interestingly, this is the reverse of the top four guitar string notes. 

The banjo?

A Tenor Banjo has only four strings. It uses the same tuning as a five stringed banjo, except the short fifth string is tuned to G (the itch is above the high D string pitch). 

The Tin Whistle? 

It is a different beast, but it follows the same principles and concepts. 

C natural can be played by covering half the top hole or by placing down the middle and ring fingers of your left hand.

Can you play the blues on a Tin Whistle? Sure, just use an abbreviated pentatonic scale. The ring and middle fingers of your right hand go on or off at the same time.

With an understanding of where the notes are on the music staff and an understanding of where they fall on your instrument you can begin to cipher how the two are interrelated.