Note: there are no 100% ways to make you completely unknown on the internet, there is always a way or another to get your identity.
Here are some ways to leave least traces possible while using the internet:
VPN : connect to the outer world using a VPN server, that might redirect all traffic to the server first, then to you, revealing the server's identity instead of yours.
Onion Networks : connects to the outer world using a set of relays, the most famous one is Tor bundle, it passes all your http/s traffic to a group of relays in order not to make a direct route between the client and the server, thus leaving the server with the least info about the client.
Onion Traffic : connects to the outer world using a set of relays, the difference between this and the previous one is that onion browsers only let you surf the internet using http/s protocols, while this can redirect any of your TCP/IP traffic into a set of relays. An example of such tool is Tails OS.
Social Engineering : do not surf social networks, do not watch web videos, do not install browser plugins, do not use unknown tools, do not download files (even from trusted resources, I'm still winning the bet that none can really guarantee 100% that a resource is safe or not on the internet).