If someone is going on a trip they usually just post a topic in the "Planning a trip?" forum saying "This is where I'm going, this is what you need to bring, this is where we are going to meet. Who's in?".
Sometimes it gets a bit more formal than that if you want to start covering your arse, but that's up to the person organising it. If you want to go that way then you generally start to list the safety equipment that is required, state that they need rated tow hooks, etc, etc.
If you go back on some of the other posts in that forum you will see some examples. But most of the time it's just an informal "come and have a play" type invitation.
P.S. Lets not turn this thread into another argument about how formal/informal it should be the rest of you! If you want to read a lengthy debate about liability, etc look
here.