Unless you go to an establishment like Starbucks, the mall, a wireless service is going to cost you.  I think you misunderstood what you were told.  You will need to get an account from an internet service provider (ISP).

Ok.  Even if I have a router?(Netgear)

Also, when I go to the mall or Starbucks, do I need a certain cord or anything, or does it automatically work?

Do you have an account with an ISP?  If so,the router will connect to either a cable or DSL modem.

 

Some helpful links:

http://www.pcmag.com/article2/0,4149,1277020,00.asp
http://www.microsoft.com/windowsxp/using/security/expert/bowman_wirelesssecurity.mspx
http://www.microsoft.com/athome/moredone/wirelesssetup.mspx

 

I have an account through my cable company for my home desktop computer but it's not a wireless service. When I am travelling, should I be able to connect with that internet service?  If I connect my modem to my work computer, should I be able to connect?  If I am travelling in the car, I am assuming I need a wireless ISP.

A wireless router at home will allow any of your machine to connect wirelessly.  When you are traveling, I doubt your current service has any access away from home.  Most hotels have free service and places such as malls and the like offer free service.

Your laptop will need a wireless card and more than likley has on ebuilt in, if not a PCMCIA wireless card can be added with little or no trouble.  Those links I posted offer some information.

you can connect near any location that offers a wireless connection, such as starbucks...however, if you want to travel, you do need to get an express card, such as through verizon, and pay for service...that way you can connect anywhere at anytime, and you can also purchase the connections so you can get internet access using your cell phone...