Everything online is interconnected, so I would take advantage of that. For example, on Facebook you can link your Instagram account. You can link your blog to your Instagram account, and your Instagram account to your blog. By linking everything, the online reach goes further, theoretically gaining more views and followers.
I would also suggest following accounts with similar interests and circles, and perhaps a few accounts outside of these interests. If the subject of your account has neutral associations (for example a DIY arts and crafts account) I would stay away from following heavily weighed topic accounts such as political affiliations and other controversial accounts. If someone were to see what accounts you are following, they might not want to follow a brand or account that has certain views. By keeping clear of strongly tied accounts, your audience might be more open to following you.
Continually post on your account, but don't post more than once or twice a day. People might not want to follow someone who fills up their feed with all one account.
Use holidays and hashtags together to reach people celebrating the holiday.
There are some Instagram accounts that claim they will get you a large amount of followers, but I don't think that is a good idea, just because I think it seems too good to be true. But that's just my personal opinion.
I hope this helps!