What is the price of CiviCRM?
CiviCRM is open source, so the software itself is free to download. So depending on your skills and availability of hosting it could be free. 

In practice, hosting costs (a bit of) money. It will cost your organisation time to learn to use CiviCRM. And if you would want extra help you would pay it to one of the CiviCRM Partners you could hire. (The Partner list can be found here: https://civicrm.org/partners-contributors.)

If your organisation starts using CiviCRM you could help support the CiviCRM community by a (yearly) donation or by becoming a CiviCRM member (https://civicrm.org/become-a-member).

But all that is voluntary and completely under your own control.

When you like CiviCRM at first sight you can get more hands on experience by looking at http://demo.civicrm.org.

After that you could try to download and install it (https://civicrm.org/become-a-member).

Let us know if you need more information.