I don't use network solutions myself but here is the general idea.
Before you get your domain to work you need to have it in a DNS somwhere on the Internet. If you don't host your own DNS you can go to www.no-ip.com
and they will host DNS for about 20-30 USD / year. After you have your domain in a DNS you must log in to your settings on Network Solutions and Add the address to your DNS Servers.
ex. ns1.no-ip.org, ns2.no-ip.org.
If you use dynamic ip (DHCP) you need to download a daemon from no-ip that constantly updates your ip with the DNS. (easy install)
After all this, count on up to 72 hours for everything to work.