If your friend's computer is set up to act as a proxy server you can only use the proxy as long his machine is running.
If you want to visit the site instagram.com via a proxy it works like this.
You send a request to view the site to the proxy server.
The server sees this, sends his own request to instagram.com
The proxy server gets a response from the target site.
The server sends the response to your computer.
Instagram.com opens in your browser.
( YOU => PROXY => TARGET => PROXY => YOU)
If the server is set up in the right way Instagram will only see the request from the proxy server not from you.
First find out which OS your friend is running.
For Linux tools check ryanfallah's
post (there is a thread on here about how to setup a server with 3proxy)
For Win there is a software named freeproxy, but I never worked with that
I have no clue which software is used for OSX.