If a Contact item is set up as a child to a parent Account then the Account must be found in order to create a new Contact but if a Contact is set up as a standalone list item this procedure will not be required.
Add a new Contact using the New Item Wizard
If the Contact is set up as child item to a parent Account then the Create New Contact process will need to find the Account first.
From an Action Bar on the Account or other Display Page
From Quick Actions
From Quick Search
From a Contact Sub-Grid
From the Main Contact Field on New/Edit forms