Dont know if you can lvl up from Honor lvl 0, but if you can Maybe try playing a few Bot Games and roam like crazy.
Out of my group of friends, I was one of the first to get to Honor lvl 5. I played a lot of bot games (because my internet sucks at home and would lag constantly). It is really easy to get at least 1 honor per game. I played like Galio, Shen, Soraka, or roaming champs. I just ran to a lane ganked and then went back to my lane. I was able to get a fair bit of 2-4 honor games that way.
Also Be nice in chat.
Again dont know if you can move up from honor lvl 0, but if you can then that would be my recommendation.
(Edit) you can increase your Honor Lvl. Play bot games as a roaming support. And be nice in chat. Since it is a bot game you/a team mate can easily 1v5. I would suggest playing someone like Galio, where if your team all suck, then you can just go dmg and carry your self. Just make sure not to flame.