One of the properties of a network is that any device on the network can send files to any other device on the network (unless the router is configured to block traffic). This means that bypassing the print server (computer next to the printer) becomes as easy as figuring out the ip address of the printer and sending it the file. Finding out the ip address of the printer is relatively easy. Most printers have a function to print out their settings. So in order to find the ip address, just browse through the menu on the front panel of the printer until you find an option which says 'print configuration/settings' and the printed page should have the ip address of the printer.
The next step is to get the file we want to print into the right format. To do this in Adobe Acrobat, simply go to the regular print page and place a tick in the 'print to file' tickbox in the bottom left hand corner. The file will appear in the same place as the original document. Now to send the file to the printer. First:
Open an FTP connection to the printer, (at the command line) type:
ftp open [the ip address of the printer]
Once you establish the connection, send the file:
put [path to the printable file]
And that's it! The printer should automatically print the file upon receiving it, no login, no charge.