If its multifunction hp laserjet printer then you can directly connect it to the network i.e is LAn.What i mean to say is dont connect it to any other linux/or windows machine but connect it directly in LAN.Assign some IP address to it for example:192.168.1.10.
Now to see if it works fine and is in network then do this:
2.try to browse it via firefox http://192.168.1.10
Now to connect Linux systemd wired or wireless follow these steps:
#yum -y install hplip*
After installing HPLIP packages:
and follow the instructions.
The Hewlett-Packard's Linux Imaging and Printing software (HPLIP) software supports 1,952 HP printers on nearly any Linux distribution available today.
For windows i think you already have drivers and just install it as network printer or standard tcp ip port.
For any other clarification revert back.