How do I see a therapist without having healthcare?

There is an organization dedicated to helping individuals find affordable counseling.  It is called Open Path Collective.  There is a one time membership fee of $49 and it lasts for your lifetime.  You then have access to local counselors/therapists who will see you for an extremely reduced rate, anywhere from $30 - $60.   https://openpathcollective.org/

There are plenty of online providers within the mental health field that would me more than happy to speak with you immediately.  Many of them provide treatment on a sliding scale fee.  I would google online mental health treatment providers and that should lead you to a list of providers that can help you. 

Depending on your area and location, there may be therapists who provide services on a sliding scale. Additionally, churches will often times offer counseling for free or for a small fee. I suggest doing a simple Google search and contact therapists in your area. It never hurts to ask for a reduced fee and even if he or she is unable to provide the service, they may be able to refer you to someone who can.