Publishing in journals with a subscription business model that allow depositing in the institutional repository will not cost you anything, since the costs are covered by subscriptions; this is the so-called green road to open access, although the articles will generally be subject to a period of embargo.
Publishing in green road open access journals (i.e. without a subscription model) will often not cost you anything; check the free open access journals in DOAJ. In other cases, the publishers will charge a series of costs, known as Article Processing Charges (APC); check in the DOAJ. All the journals found on this portal are quality checked and peer reviewed.
Visit the journal's website for specific cost policies.