One of the best ways to do this is through advertising. You can self-promote your site using Facebook, Twitter, Google +, posting on forums in your YouTube niche, and through paid advertising sites. There are a few forums online that will pay you to post on the forums. These are normally money making forums like Beermoney Forum. On this site, they have a job board where you can pay people to go to your YouTube channel to subscribe and follow you. This will help to generate traffic to your site. They also have traffic exchange sites that you can join to drive more traffic to your YuoTube channel.