They will never be totally separate, but there are standard options in the "Multi-company" section under "General Settings": 

If you uncheck "Common Contact Book" and "Common Product Catalog" then each company will have its own products and contacts (customers, suppliers).  These use Record Rules. 

There are other Record Rules that will limit what users can see and do, but be careful because they don't apply everywhere (e.g. Leads in CRM in version 11, and events in the Calendar). It's easy enough to create new Record Rules once you know what is missing.

Private Addresses are something else (more information here).

Note: this answer refers to Odoo 12 and earlier.  This logic has changed in Odoo 13

['|',('company_id','=',False),('company_id','child_of',[user.company_id.id])]

Hi. You can perform it by using Record Rules.

Find more information here: 

\https://www.odoo.com/documentation/12.0/reference/security.html#record-rules