After boot up
The following instructions are for Linux, although the general idea should work for other operating systems. The links below do provide instructions for other operating systems.
After your computer has booted up and connected to the internet any and all information is passing through your ISP. Depending on various factors, of course, your ISP may have little to no access to the actual information exchanged between you and the website(s), email servers, and other services you are visiting. But the metadata, information like the website or service your visiting are visible. Your ISP is collecting that information. One way to anonymize yourself is to use a VPN. But even then your information about the sites you're visiting can leak. Hence I would also advise using something like dnscrypt. One final measure would be to change your MAC address by using a tool like macchanger (note that you likely have to change your MAC address prior to connecting to the Internet, especially on a WiFi network).
BTW, this concerns not only your computer but any device in your home - Amazon Echo or TV, Google Home, smart TVs and any other internet-enabled device. All of these are providing information to your ISP about you. If you can set up a VPN on your home router you have provided an additional layer of security.
I use OpenVPN and have set up my own dedicated VPN server. There are many services out there that provide VPN servers, but be very careful about choosing a VPN. One free VPN service that is good can be found at: https://www.vpnbook.com/freevpn
2. DNSCrypt or Cloudflared
I used to use dnscrypt-proxy, but have since moved to cloudflared as it works better for me. Try them out and find what works best.
dnscrypt-proxy is available at: https://dnscrypt.info/
Cloudflared and instructions are available at: https://developers.cloudflare.com/18.104.22.168/dns-over-https/cloudflared-proxy/
If you're only concerned about DNS security while browsing, Firefox now offers secure DNS. Go to Preferences and type in the search: DNS. This will take you to network settings. Check "Enable DNS over HTTPS."
After enabling VPN and DNSCrypt, check what information can be gleaned from you by going to:
IP Leak : https://ipleak.net/
Whoer : https://whoer.net/