Most Helpful Girl
You have to use some kind of mobile or tablet device to set up your account.
Once you've done that you can use websites, like Webstagram to browse, like, comment and search for people's profiles. Not 100% sure if you can post a photo from those websites though.
Most Helpful Guy
Im not sure if this would work but you could try one of those free texting applications that assign you a number and then use that number when creating your instagram account.