How do you find the SSID for the network?

I clicked on my tool bar and bring up the net info. It says Network name(SSID) then a name, but when I type it in to my new computer when it asks for it, it just blows it off and asks again.
It is not a number is it?

It can be a name or a number - or any combo of those things.
You can also have various levels of security on the wifi including:

(common) password protected (wep or wpa)
(not common) hidden SSID (so you need to KNOW the SSID in order to join - it wont show up in a list)
(very uncommon) MAC filtering on the router (meaning the router must have the MAC address of your computer entered in it to allow access)

SSIDs are generally case sensitive - so be sure you're using caps where caps go - and lowercase where lowercase goes

I called up the wireless Lan utility and it says
SSID then it says something, but when I type that in to the new computer I am trying to get setup on the network, it does not recognize it. It is a hidden network.

Okay, I got it, I was doing something wrong, but now it is asking for the network security key for the hidden network

Edited to say that is just another name for password...geeez.

that would be the:
(common) password protected (wep or wpa)

To get that you'll need to log into your router or modem (whichever is broadcasting the wifi)

The SSID is whatever the network is called/named.
It is possible that the SSID is hidden from broadcast...