It might seem like a silly question to someone who has played the banjo before, but almost every time I give banjo picks to someone who has never played before, they put the picks on backwards. Banjo picks are worn by 5 string banjoists who are playing the 3 finger style. There are some clawhammer players who use a pick as well, but here we will be focusing on 3 finger style 5 string banjo players. In this style, players use a thumbpick and two metal fingerpicks.
The type of thumbpick used is almost always plastic for the pick part, but the wrap that holds it to your thumb can either be plastic or metal. When you put the pick on you want the pick to be pointing away from your hand. If you are right handed and your hand is flat down, the pick would be pointing to the left. You want to push the pick down onto your thumb so it sits comfortably somewhere between your thumb knuckle and the top of your thumb. The thumbpick is pretty straight forward as to how to wear it.
The fingerpicks are where more people get it wrong the first time and there are more questions and techniques people use to get the best possible tone out of their banjo. Most people when putting on a fingerpick for the first time put it on as though it is a fingernail. This is incorrect. If you put the pick on like this you will hook the strings every time you try to play as oppose to glance off of the strings. You want to put the pick on to cover the flesh part of your finger and it will curve up towards your nails.
How far down you put the pick onto your finger varies and is personal preference, but I try to push it down so just a little bit of the pick sticks out beyond my finger. It sticks out maybe about 1/8 of an inch. I then bend the part that is sticking out just a bit to curve up a little bit more. I feel this gives me a cleaner tone with a bit less pick noise and allows me to play through the strings easier.
One other thing I do is to very slightly twist the pick to the left (if I am right handed and my hand is facing flat down). This allows me to strike the strings with the pick more straight on because when my hand is in the playing position, it is at an angle and my fingers naturally want to strike the strings at an angle. This causes pick noise and a less clear and full tone. By twisting the picks just a bit it helps to alleviate this. The fingerpick maker ProPik makes a fingerpick that has an angle built into the pick which helps to alleviate this issue as well.
There is no hard and fast rule as to how exactly to wear your picks (how far down, bent, twisted) as everybody’s hand is slightly different, except for the direction the pick is facing, but this is what I find works for me. Experiment and see what works for you and continue striving towards playing with the best possible tone.