As of 2015, it is only possible to create an Instagram account through its mobile app on a iOS, Android or Windows Phone device. The process involves either providing an email address and username or by signing into a Facebook account and linking the two.
The first step to creating an Instagram account is to download the official Instagram app from the appropriate smartphone app store. After downloading the app, the user needs to open it and tap the Sign Up link beneath the area that asks for a username and password. On the following page, the user is able to choose between linking the account to a Facebook account or an email address. If she chooses to use an email address, the must enter it in the appropriate field and tap Next. This takes the user to a page where she must create a unique username and password, then manually fill out her profile. This includes her name, which does not have to be her real name, and a short biography and then tap Done.
If she chooses to link to a Facebook account, she must tap the Log In with Facebook button and then authorize the app to access the necessary information from the Facebook account. This fills in her name and details, and also sets that as the primary recovery method for lost usernames and passwords.