You just need a small file, like a point file. Any gasheads remember those? And a single edge razor blade or the like to lift the reed.
To raise the pitch, you file the end of the reed, making it lighter so it vibrates faster.
To lower the pitch, you file near the attached end of the reed. I am not sure on the physics of this and would appreciate anyone's insight.
The specific tuning I've done many times is to convert a standard diatonic harp (the Richter tuning) to what is now called the Melody Maker tuning.
The Richter tuning was apparently designed for "campfire songs". You could just "blow, man, blow" and all the chords would sound OK.
Later, blues musicians discovered that you could emphasize the draw notes, the ones that are easy to bend to a flat note to get that bluesy sound. This is called "cross harp". For example, in a song in G you would use a C harp instead of one tuned in G.
The problem with cross harp is that the 7th is a minor 7th and you have no way to raise it up to a major 7th if that would fit your song. And the 2nd is completely missing! In fact you just have the tonic (G in this case) on both the draw and blow notes where you might hope to hit the 2nd (A). There is no A in this scale, only the G twice.
To imagine a song where this may be a problem, think of the first three notes of the Beatles song All My Loving. It starts with 3-2-1. Oops, I ain't got the 2. Just the 1 twice.
This is where the file comes in. You raise the blow 1st to a major 2nd. And you raise the minor 7th to a major 7th in both octaves.
Now you have a harp with that bluesy sound we all love, but in a major scale!