When you set your systems to the 'obtain an IP address automatically' setting, you were configuring them to look for an address provider. A computer with this setting will give itself an IP address in the 169.254.xxx.xxx range, but this is considered a temporary address, and the computer will periodically send a message to all connected devices, looking for a DHCP server to give it a different IP address.
Within about 5 minutes of configuring your computers, they should all have acquired an IP address from the router. Along with the address, they will also have been configured to use the router as their default gateway out of the network.
At this point, assuming your router is connected to the Internet, all computers should have internet access.
If you have verified that your router is connected, but some of your computers are not getting Internet access, chances are that they haven't picked up an address from the router yet.
To check this, go to the command prompt (start/run 'cmd' in XP/2000, or start/programs/ms-dos prompt in 98) and type 'ipconfig'
What you are looking for is the IP address. It should be in the same network as the router's IP. For example, if your router's IP address is 192.168.1.1 with a subnet mask of 255.255.255.0, then all the computers on your network must have IP addresses between 192.168.1.2-254 in order to communicate.
If, as in the picture above, it is a 169.254.xxx.xxx address, or it is simply 0.0.0.0, then the system either has not yet picked up a DHCP address from the router, or there is a connection problem. To verify this, type 'ipconfig /release' ('ipconfig /release_all' on win98 systems), followed by 'ipconfig /renew' ('ipconfig /renew_all').
If the system is able to communicate with the router, you should have attained an IP address from the router's pool of addresses.