Practice tuning! This is a skill we must develop to a very high degree. Do it every day just like learning chords and licks. Postpone the purchase of an electronic tuner. Start with a good tuning fork; A440 is the most common pitch. Set your instrument purposely out of tune and re-tune it as follows:
Tune the A string to the pitch fork. Do this by tapping it on your knee and placing the ball end on or near the bridge. First sound the string, then add the vibrating fork. Tune the string and listen for the "beat" to disappear.
Now set the tuning fork down and tune each of the remaining strings in turn, using the A string as a reference. Don't note or fret the strings anywhere and don't use harmonics, just practice listening to the two strings sounding together and learn to "hear" when they are properly in tune.
Before tuning a string, be sure it's already below the proper pitch. If it's sharp, crank it down a full step or so and bring it back up. Never tune a string "down" to the proper pitch.
I know this is boring and maybe even hard but you'll be amply rewarded. Do this over and over as an exercise until you can crank all the strings into proper tune in just a few seconds. Once you master this, you'll never be satisfied with the results of an electronic tuner.
Of course all this depends on having your instrument properly set up and in good playing condition.
For guitar I tune the A string then tune the bass E and D strings by it in turn. Then I tune the treble E string, again using the open A as a reference. Next I tune the B string using the treble E as a reference and finally I tune the G string against the D. If I've been careful, the B and G strings will wind up exactly in tune even though I came at them from opposite sides so to speak.
For fiddle I tune the A string by suspending the instrument firmly under my chin and bow the A string while applying the tuning fork to the belly with my left hand. I find that tuning a bowed string is more accurate than tuning a plucked one. Once the A string is correctly tuned, I bow adjacent strings together while twisting the peg or the fine tuner with my left hand. Your ear will tell you when the string you're tuning has "dropped" into place.
For a five-string banjo it's tough to use the A440 fork since there is no A string. You can get pitch from another musician or simply learn to tune the fourth string by its interval from A440. In any case the basic tuning technique is the same.
This tuning method does not require perfect pitch or even relative pitch if you learn to hear the "beat" caused when the strings are close but not together. The vibrating string produces harmonics of the primary note at most of the common tuning intervals.
A side benefit of this method is that you improve your ability to listen.
Hope somebody finds this useful. Better yet, I hope somebody has an improvement to the technique.
Good luck and stay tuned,