He is testing, both the boundaries and his environment. Discovering what he likes to chew on. Chewing on you however is to be discouraged. Start by giving him a gentle 'No Bite' when he does this to you. Please disregard advice to:
Yell at him
Spray water at him ( like a squirt gun)
Do anything physical to him
If the gentle No Bite does not get the message across, and he is more bonded to you, use the Shunning method. THat is how birds in the wild discipline their unruly youngsters. For you to adopt this method, when he bites with more then acceptable pressure, continue to say "No Bite" and immediately place him on a handy nearby chair back. Turn your back to him, no eye contact at all, no talking to or about him, for one minute. No less, no longer. Then you can re -approach him. In order for this to work, you must do it EVERY TIME and so do other members of your family.
. Why a chair back - why not his cage? Returning him to his cage only teaches him that if he wants to go back to his cage, bite the person.
. Why immediately? So the lesson can be connected to the biting activity.
. Why only a minute? Any longer and again, the lesson will not be connected to the bite activity
. Why no talking to or about him? Parrots are SMART and certainly know their names and when you are talking about them
. Why every time? So you do not confuse him with mixed messages
Most parrots, even young ones, get the message quickly when it is done correctly. And you must keep it up their entire lives, not just when they are young 'uns. They constantly test boundaries and try to see what they can get away with, and with mating season mood changes they can get 'bitey ' too.
Conures in particular are known as a 'bitey' species so its important you stop this in its tracks.
Good Luck!