Find the nearest rifle club and get both yourself and him memberships. My late dad bought life memberships for both myself and my son.
Bring your son to the junior matches. This is important that you show enthusiasm for it as well.
Practice yourself at the club.
Buy .22 rifles for each of you.
If your address is NE = New England then we have matches here all winter when it's too cold to shoot outside.
The rifle matches are on Thursday night and pistol the next Thursday.
