How exactly is the best way of getting this done? Can some people share some tips, with semi-detailed explanations please, along with maybe some tools that you use to help you grow your rank.
The only way I know to grow your feed count is by posting quality content. You can offer incentives like ebooks for your subscribers as well.
Create good content that makes people want to come back to your blog, I recently jumped 38 subscribers today due to a free ebook I created.