Private accounts are only visible to your friends. The first step in gaining Instagram followers quickly is to make your account public. If you are concerned about privacy, you can always check what you share.
Yet another tip to increase your visibility on Instagram is to follow others. They might follow you in return. You can go one step further and like and comment on videos and photos of others. You're likely to grab the attention of the photo owner as well his/her followers. This might encourage them to visit your Instagram account, which could increase the chances of you getting more followers.
It's a great way to increase your Instagram followers. A more active account will be more engaging than one that is inactive. Plus, using Instagram to share all types of content with your audience in many forms is going to be much more interesting to them than if you shared only one type.