Since ICANN is no longer the only top-level domain name registrar, I doubt that this will be nearly as catastrophic as some predictions. There are several other top-level domain name registrars.
If you are concerned, start storing the IP addresses of the sites that you visit in your /etc/hosts file. This is how the Internet worked BEFORE we had domain name servers (DNS). The PING or WHOIS tool can be used to get the IP address of most sites.
# 123.456.789.012 mydomain.com 220.127.116.11 billstill.com 18.104.22.168 youtube.com
If you have a website, you may want to publish your IP address on your home page for the next few weeks, and create a mod_rewrite (.htaccess) rule that rewrites incoming URLs that include you site’s IP address to your domain name. This is probably the easiest way to keep sites functioning if ICANN disrupts normal DNS lookups. -Ed.