There are a few ways to send yourself a test message,
create a new client profile with your own phone number
click on "contact" to start the conversation.
or if you subscribe to the plan includes auto message only (no 2-way message included), try create the first appointment. Once the appointment is created, there will be a pop up message asking you "Do you want to send confirmation message to this client?", hit "yes", so you will receive this auto message.
This option is even faster than Option 1.
If you have just registered MoeGo account, you will see a demo profile named as "Profile demo" in the system. You can go to that profile page, and change the phone number to your own phone number. Then click "Contact" button to initiate the chat.
Also here is how 2 way message and auto message works in live action: