Here are a few tips to grow your brand on Google+

1. Set up rel author to all your blog content - this way you can link your G+ account to external content - https://support.google.com/webmasters/answer/2539557?hl=en
2. Join in relevant communities on Google+ - https://plus.google.com/communities 
Join in discussions on the communities and make your self known.
3. Follow relevant people in your industry if you see a chance to help them do it, it can mean re shares of content or any thing.
4. Start your own community on Google+ and share content via it, I run a community with 7k members.
5. Try and get included in relevant niche specific circles on Google+ people make them and then share them via the network you can gain 100s of followers via this.

Any more specific questions please ask me, I have been using Google+ since the day it was released ;)

I would also suggest using Google Hangouts - it creates a video for your youtube channel as well lifting your SEO ratings.

In addition to Jame's answer, Since your Google Plus account will show up on Google searches, so make sure you keep posting things and up to date!