Setting up shared computers on a network is fairly easy. The computer attached to a printer (usually via a USB cable now) needs to have file and printer sharing activated and sharing enabled for the printer (In printer properties) . The target computer then just needs to run the add printer wizard in the printers folder. The wizard will even install the printer driver from the computer sharing the printer.
Printers that sit on the network (that is are plugged directly into a switch or router) are a different matter. Many have a client program that will help locate and install the printer but some do not or the software is flaky and doesn't manage to find the printer.
The first step is to ensure that the printer is setup on the network okay. To do this you need to find out what the Network Address is for the printer. Go to the printer and generally somewhere in the menu is the ability to print out the network settings. This should include the IP address (This is the series of four numbers separated by a dot).
You usually can setup the printer via the printer console but this is usually painful. Go back to your desk open up the browser of your choice (tried Chrome yet?) and type in the IP address of the printer and you should get the setup page for the printer.
If you can't see the printer's web page, it is possible that the address has been fixed to be in a separate sub-net. Check the IP address of your computer. This can be done by going to accessories and selecting the command prompt. In the command prompt type type in ipconfig.


The display above is an example from a Vista computer. Note the first three numbers of the IP address they should be the same. If the first three numbers are different you will need to change the settings at the printer. The first thing to do is the change the address to a fixed address rather than one determined by  DHCP. Each printer is different but generally it will either ask if you want to have a fixed (or static) address (the answer is yes) or it will ask if you want to use DHCP (the answer is no).
It will then have a spot to enter in the address. The address will need to be outside the DHCP range. If you don't know what this is then it is pretty safe to use a high number as the final digit. For my network I could use 192.168.50.200. If you have a problem with a printer disappearing from the network, it is usually because an address has been chosen which overlaps with another address.
Now that the printer is setup, you need to then put it onto the computer. First install the drivers for the printer. You can use the disk you got with the printer, but I prefer to download the latest drivers from the manufacturers web site.
After the driver is installed run the "Add a printer wizard". However instead of selecting

Use the Add a local printer. The picture above is the Vista version but the XP version is similar. On the next window select create a new port and select "Standard TCP/IP port".

The next window will ask for the port name and address. Type in the fixed address that you gave the printer and hit next again. The computer will then try and identify the printer. I find that the computer is usually unsuccessful at identifying the printer. Just select the printer you installed from the dialog and finish the process. Don't forget to print the test page.