I'm not sure if multiple account signup is currently supported in Instagram mobile app and sign up is not available except through the website. There was once single phone can create only single account restriction. If you are unable to create a new account from your mobile app and if you dont have two phones, then the only way to create a new instagram account in a computer is to
Install Bluestacks or Andy Emulator for computer -> Install Instagram App -> Create a new account.
And access the created account in a browser or in the emulator itself.
If you have a Lollipop OS you don't need two phone nor need to setup Bluestacks. You can install Instagram app under two different User Accounts and both Instagram apps share a different appdata and therefore different username to login with.