This is a caddy:
Amazon.co.uk User Recommendation
You can remove the bottom from your laptop to get to the disc - sometimes there are screws, sometimes it will just slide off.
Remove the disc, insert it into the caddy and connect to your new computer with a (supplied) USB cable.
The caddy I showed is USB 3.0 and I have 3 or 4 of them. Otheres are available but I've found that one reliable, fast and easy to put the disc in as no screws are involved.
You might have to do a little work to get the new computer to accept it since it has been a system disc. It's straightforward and quick and you will find help on here if it needs doing.