1) Find a quiet place

First, find someplace quiet. I know this is obvious, but I couldn't leave it out. Avoid ceiling fans, in particular, which disturb the sound waves and make the notes waver.

2) Stretch the strings

Make sure your strings have been stretched if the 'harp has been sitting a while, especially if it is new. This is a tedious process: tune reasonably close to standard pitch, push and pull on the string, check the tuner, then tune again; repeat this procedure until it holds, usually two or three times. (Often this method can be used to "fine-tune" a note, lowering it 2.5 cents or so.)

3) “Rough tune” first

Do a rough tune first, putting all the notes "in the neigh­borhood", before trying to fine-tune; this will evenly distribute the tension on the 'harp.

4) Go through the circle of fifths

If sweet-tuning by ear for key of F, go around the circle of fifths, starting with f, using the harmonics to give you the perfect fifths and octaves. Keep in mind the d,a,e, etc. should be flattened slightly so they will fit in as thirds. You could also do this by obtaining the #1 and #5 notes for each major chord and then tuning the middle third note to the other two.

5) Favor high needle jumps

If you're using a tuning machine, tend to favor the higher jumps of the needle because in melody playing the initial onset of the note is what you'll hear most often.  This is especially true of the bass notes since as the vibrating string returns to stasis, the meter will show a progressively lower pitch – so if the “settling” point is lower than its octaves, the initial wider vibrations will be closer in pitch. Better yet, strike the string you are tuning repeatedly in a steady pattern, like you were counting beats: 1…2…3…4… This gives you the attack without the decay and is more like what happens while you are playing.

6) Install a fine tuning system

A set of fine-tuners (available from a number of parts dealers/repairmen) is expensive and takes a while to install but saves time and anxiety in the long run.

7)  Use the direct in

You can get a clip-on tuner pickup or alligator-type clasp and fasten it to a tuning pin somewhere among the mid-octave strings .  This will transfer string vibrations fairly accurately to the frame and avoid any outside noise from the room.  Also, gently rest your palm on nearby stings not being tuned to keep sympathetic vibrations from confusing the electronic sensors.

8) Zero point is arbitrary

When you start tuning, check the different notes to see where they have settled and remember that the less you have to alter the better, and that, unless you are playing with other instruments, it does not matter which note is assigned the "zero" point as long as all are in tune relative to each other.  Strings have a “memory” and will want to return to previous tension, so the less you have to change it, the more likely it is to hold.

If you are going to be playing in an ensemble with other instruments, you will want the tonic notes of whatever keys will be used to be at zero on your meter.

9) Check m7 arpeggios

Once you think you've got things right, check by playing minor 7th arpeggios made up of notes from the I and VIm chords (C+Am = c e g a = Am7;  G+Em = g b d e= Em7, etc.)

You don’t actually have to have an Am7, for example, just pick the strings from the chord and let them ring.  They should not clash too much.

10) Clean your strings

From time to time, use some kind of commercial solvent (like Fast Fret or a spray-on-cloth type for guitar strings) to get the grease and grime off your wires.  Assuming you pluck with your fingernails to get the note and/or tune with harmonics, the oils from your grubby little mitts get on your autoharp.  The build up can cut down the vibrations and distort the readings of your strings.  So wash your hands before tuning.  Actually, wash your hands anyway to keep from catching a cold.