if they are encrypted (using my private key)?
Messages are not encrypted using your private key (or any private key at all). They're only decrypted using one.
(They are, however, signed using your private key – but that's a separate feature in S/MIME and is not to be confused with encryption! The contents of a signed message may be packaged in a way that looks similar to an encrypted message, but that does not mean any of it is actually encrypted.)
how do the recipients get my certificate so that they can decrypt my mails?
Recipients do not need your certificate to decrypt your mails. They only need their own certificate – or rather, the private key that goes with it.
Instead, you need the recipient's certificate so that you can encrypt the message for that particular recipient.
So it does not make sense for you to send anything together with the message (certainly not a private key – the whole point of public-key systems is that the private key is never sent anywhere, ever); instead the recipient has to send you their certificate first.
You might be confusing S/MIME encryption with signing, which is opposite in many ways: you use your own private key to create a digital signature, and the recipient indeed needs your certificate so that they could verify that signature. (But not necessarily to read the message – they can just open it unverified if they wish. Indeed most people receiving a signed message don't verify it.)
When signing messages, your own certificate can indeed be included within the signed data; I believe most mail apps do so by default with S/MIME. This works under the assumption that your certificate has been issued by a CA that the recipient "trusts". (With OpenPGP it's also an option but not as common, due to the different nature of OpenPGP certificate verification.)
This is also one way that you can collect certificates for encryption – the other person sends you a signed "Hello!", you verify it, and hopefully, your mail client stores the person's certificate in the address book. (At least some mail clients have an option to do this, manually or automatically.)