A lot depends on the age and style of the instrument.... the really older types (light weight, usually black bodies) are more 'delicate' and can warp. Newer styles in brown/blond woods made after the 60s are usually stronger. *IF* you have an older one, be very careful if you ever replace strings to match the string diameter, as newer strings are heavier and can warp an older instrument.

A digital tuner is easily the best way. I prefer the older style with a 'hand', rather than just digital read-out, but just be sure it will handle all octaves.

If the 'harp hasn't been tuned recently, go slowly! I suggest tuning all of one note... that is, all the Cs, then all the C#s, then Ds,,,etc. to even out the stresses. (An autoharp has a large amount of pressure from all those strings.)
Once you get to the last strings, it will almost surely need to have the first ones adjusted as the wood AND the strings respond to the new settings. After a few playings & retunings, it will settle in and, if played & retuned semi-regularly, will not need as much adjustment. Still- weather and humidity changes will affect it, just as on a guitar, but over 6 times as many stings of very different length.

Tuning is easier using a T-handle wrench which fits well, as the L-shaped wrenches are a bit harder to get exactly the right amount of torque/pressure. (I prefer an 8-point, rather than 4-point wrench, as they tend to slip less.)