First of all I really think you need to identify what is exactly going on with the private key-certification:
- Private key: this is something you must keep secret, for your eyes only.
- Public key: this is something users will use so they can contact you (it is like you are using a language only the private key owner knows).
- Certificate: this is something to validate that the public key it is actually the one associated to the owner of the private key.
So, consider that a certificate is something public that you can give away without being worried about that.
How does a certificate work? Let me put it in simple words: when issuing a public key, the CA adds a "secret mark" to the certificate, so when you want to validate it you have to send the certificate from the owner to the CA so it can check if the "secret part" is ok. If the CA checks the secret part and is consistent it will give you the "OK" to use the public key if not you should be suspicious about using it.
Consider having a look at this wikimedia diagram so you can learn about the whole process of creation and validation (CA included):
This other diagram might be useful as well:
Also, consider that the CA are usually well-known trusted agencies and normally browsers have a list of them included. But some entities (usually public agencies or organizations) use their own CA and you have to manually add it to the list (please be extremely cautious about this since a malicious CA could really compromise your communications).
Hope this helps you.
(Feel free to add any grammar/syntax correction since English is not my mother tongue).