Some tailpieces have hooks that are hard to reach, or that don't hold the loops too well until the string is tuned. Bend the loop to fit the contour of the tailpiece if necessary. Hold the end down to the pointy end of a pencil and just roll the loop around:
You'll get a nice smooth bend that way. For more about bending loops, check out the mandolin restringing article.
Then, just slip the loop end over the hook:
And run the string up over the tailpiece, and under the bar in front:
I'm holding the string down with my finger and slipping it under the bar.
If your string has to go down through a hole in the front of the tailpiece, just bend a curl at that end of the string so when you insert it into the tailpiece it will be easy to grab and pull through. Also, that way you won't be likely to poke a hole in your head:
Here comes the nasty part. All instruments with tailpieces have movable bridges. That means when the strings come off, so does the bridge.
It's important for all banjo players to know how to position their bridges.
The conventional method of placing the bridge is to play the harmonic of the first string at the twelfth fret and compare to the fretted note. If you just barely touch the string directly over the twelfth fret and pluck the string with your finger, you'll force the string to vibrate at exactly the octave note:
