For years it’s been simple to set up DNS on a Linux machine. Just add a couple of entries to /etc/resolv.conf and you’re done.

# Use Google's public DNS servers.
nameserver 8.8.4.4
nameserver 8.8.8.8

But things change and now it’s not that simple. If you now edit /etc/resolv.conf on Ubuntu you’ll find that the edits are ephemeral. If you restart (or even hibernate) your machine then they’ll be overwritten by default content.

nameserver 127.0.0.53
search Home

This is pretty simple to fix though.

1. Install the resolvconf package.

sudo apt install resolvconf

2. Edit /etc/resolvconf/resolv.conf.d/head and add the following:

# Make edits to /etc/resolvconf/resolv.conf.d/head.
nameserver 8.8.4.4
nameserver 8.8.8.8

3. Restart the resolvconf service.

sudo service resolvconf restart

Fix should be permanent.

Source: DNS on Ubuntu 18.04 – datawookie