After what feels like forever, multi-account support will arrive to Instagram in an update this week. After some people received the feature recently, the rest of the world gets to join in very soon.
Instagram will make its server-side changes that will find their way into v7.15 of Instagram or higher, but with the Play Store version of Instagram already at v7.16, it can be confusing. This means that multi-account support isn't hitting everyone just yet, but it will be enabled very soon.
In order to get multiple accounts working within Instagram, you'll need to tap your username at the top of your profile, which will then let you change accounts. Your profile picture will be used throughout the app, which will let you keep tabs on which account you're signed into at that moment.