If printing/printer coordination is included in the proposal, contact a printer at the beginning of the project (or before writing the proposal, if necessary).
Project specs to give the printer:
Once the printer gives you quotes, put them into a proposal for the client.
Send the proposal (or printer quotes, if retainer client) to the client for their approval.
When final files are done and approved by client and Art Director, send the print-ready files to printer.