Different ASUS router models using different firmware versions will have somewhat different user interfaces. Here are some general instructions that should help.
First, go to your router's settings page by typing 192.168.1.1 into your web browser. Either one should work. The default login is username: admin, password: admin.
In the left navigation menu, under Advanced Setting, click on WAN. This should open up a page entitled "WAN - Internet Connection".
Find the section entitled "WAN DNS Setting" and check that "Connect to DNS Server automatically" is checked.
You can also use Google's DNS 188.8.131.52 if you have issues loading some websites as a troubleshooting step.
Remember to clear your device's cache to apply the new setting. A simple way to do this is to power cycle your computer/mobile/router.