I think easiest and common solution for basic anonymity over web is to use VPN, for more secure connection we can try establish connection via few VPNs, anonymity will be really good, just transfer will be limited and connection slow. 
For beginners I would recommend some very simple VPN like NordVPN - it cost just 3,5 USD per month other simple are expressVPN, cyberghost or hidemyass. I dont recommend free pseudo VPNs via web, that's not VPNs