I am an 18 year old civilian without a law license.
Theoretically, the law allows for this. Read RSA 311:1: http://www.gencourt.state.nh.us/rsa/html/XXX/311/311-1.htm
HOWEVER, I would never recommend this to either the potential litigant or the person thinking about representation this way. It is very likely to end badly for all involved.
If you are interested, there was a fair amount of press and legal opinions on this issue about 15 years ago involving a non-lawyer named Theodore Kamaskinski in New Hampshire. Just google it.
The exception might be a family member helping with a minor matter like a speeding ticket or a small claim where hiring a lawyer is not cost effective. Even then, be very careful.