In the list of companies and contacts related to the project, click in the Company field and type some letters of the company you are looking for.
Once the company code appears in the list, select it.
The Contact field now shows contacts related to this company.
Select the appropriate contact from the list.
Now click on the "Save" button.
You can also link a contact without a company code to the project. To do this, search directly for a contact without choosing a company first.