Ok Taylor,
If you know barely anything about computers then this is going to be a long one but I'll try my best to explain how to do it.
First what you need to do is download and install the printer software onto the laptop that does not have the printer connected; that would be your laptop.
Then, find out if both computers are in the same workgroup (name). You can find that out by right clicking the "computer" on your desktop (make sure this is NOT a shortcut link to "computer") and choose "properties". As a standard the workgroup should be called simply "workgroup".
If you needed to change that, first reboot the machine that had the workgroup changed.
Now go into the control panel of the computer that has the printer connected and go the printer section. Look for the default printer, that is the one with the name of the printer and a green check mark onto it.
Right click the icon and go for properties. Then you should find the "share" or "sharing" option and choose for share this printer.
For the next step, go into your network settings into your control panel and activate the documents and file sharing options for the local profile. You can also access these options by simply going into "network" via start. In there you choose the advanced settings and somewhere in there you will see the option to turn on sharing printers and you need to turn that on.
Now, once this is all configured on the printer connected laptop, go back to your laptop that does not have the printer and go into the control panel and go the printer section. Choose "add printer" and you will be presented to add a local or network printer. Obviously go for "network" and your laptop will now search for available printers in your network/workgroup.
Add the printer that he finds and finish the wizard. Choose the printer again as the default printer for your laptop and now whenever you need to print something it will roll out without any problem from now on.
Hope this howto has been helpful to you and I wish you the best of success!