My MacBook Air is connected to my home network, but not to the internet.

Hi kevinmac0505,

Usually, your router or gateway supplies the default DNS servers for your Mac to use. If this isn't happening, try forgetting the network, and then rejoining it: How to forget a Wi-Fi network on your iPhone, iPad, iPod touch, or Mac - Apple Support

If that still doesn't work, try providing one or two of these DNS servers. There are many more to choose from, these are only examples:

Google: 8.8.8.8

Cloudflare: 1.1.1.1

Quad9: 9.9.9.9

OpenDNS: 208.67.222.222, 208.67.220.220

Restart the Wi-Fi router, and try again.

Failing that, create a new Location in System Preferences > Network, and add the Wi-Fi network there.

Probably in System Preferences -> Network -> Wi-Fi -> Advanced -> DNS.

Where are you seeing no DNS?