To add a client organization to lead, open the desired lead from Leads or Featured Leads, click on the Client tab, then click Add client:
Select the desired organization from the ones in your database, by scrolling the drop-down menu or typing part of the name in it. You can also create a new one on the spot by clicking on the + button next to the organization selector menu.
Select a Project Manager (or add one by clicking on the + button) and optionally also a Deadline and a status from Statuses.
Note that you can create new statuses for clients from Settings->Dictionaries->Lead organization statuses, on the navigation panel.