Tweet on the weekends. Research shows brands get more engagement on the weekends than during the week. Mention users in your tweets when replying to other users. People are more likely to connect with your tweets when they are mentioned by name.
Use a follow button on your website or blog. Make it easy for your website visitors to find you and this way, you get free followers. Post motivational or inspiring quotes. These are good for getting re tweets. Respond publicly when your reaction would be useful to others to attract new free followers, be sure to mention the person who asked.
Incorporate a link to your user-name in the author biography of your guest posts when doing cross website/blogs marketing. Using Social Mention, find out what other Twitter users are saying about your brand or industry.
Invite guests to post on your account based on the relevance of the topics you want seen on your website or blog. If you are connected with an influential Instagrammer, you could ask them to guest post on your account as a strategy for obtaining followers.