It took me five months to reach 100 subscribers. Another month to reach 200, and another to reach 300.
In the beginning, the few subscribers were mostly family and close friends. I tried to email all my friends, sent every parent I know Facebook messages about my channel. This was not very effective. Most people didn't even open the emails (I use MailChimp email service). Most of so-called Facebook friends didn't even reply to my message. I forced some colleagues to subscribe to my channel when they took out their smartphones.
I never did Sub4Sub or bought subscribers via Fiverr.
All of this bought around 25 subscribers in 1.5 months. So, I decided to pursue an alternative way.
I do educational videos for children, mainly about animals. So, the content is very "searchable". I try to do lots of research before posting regarding SEO (proper titles, tags, matching description). I also make attractive thumbnails in comparison to my competitors.
I post every video in various Facebook groups (parent groups, animal lovers groups, etc.). I do the same for Google+ communities. I tweet about my video. My channel has a Facebook page, where I post my videos as well, and share via my personal account. I recently made a Pinterest Page, Instagram page and even a musical.ly page (tip from Gary Vaynerchuk). I'm not using these very efficiently yet, though. Facebook is the primary source of traffic.
I tried Reddit a few times, which brought some traffic. I wasn't cooked there, so I'm happy about this.
With all these actions, my views started to grow. I have around 2500 views/day at the moment. The subscribers have grown proportionally.
It seems that patience and consistency are keys to increasing subscribers. I have 11 videos by now and a few more are in production. My biggest challenge is to make videos faster. My goal is two videos per week. I work as well with a creative friend to improve my channel art. Tim Schmoyer puts lots of emphasis on channel design to get more subscribers. For example, I still don't have a channel teaser. There is still some work to do.