I know the way to make private calls (the 31 thing) but was wondering what do I have to do to send a private message?

Are you talking about from a cell phone?
If you are, then the answer is no.

On my cell phone I have a option to allow my number be seen or to hide my number to the people I am calling.

I know its possible because I've gotten messages from private numbers before

I'm quite sure is not possible to send messages without your id. You can receive them but not from other user, but from your service provider. Or applications your service provider allowed to do so.

i know the way to make private calls (the 31 thing) but was wondering what do i have to do to send a private message?

You can hide your CLI ( caller line idenity ) when making calls over a cell phone network, but there is no way that you can send a sms(txt) message without showing your id ! The only people that can do that are cell phone networks or companys that pay for a special service but even these normal show a name or something when sending.