You generally do not require a VPN (Virtual Private Network) connection to send or receive messages or connect to the internet. If you don’t know what VPN is, or what it is for, then it is very unlikely that you need to use one.
For those rare situations where you someone needs to use a VPN, many will use a VPN “App” that automatically creates the necessary settings - instead of setting-up manually from device settings.
What type of “messages” are you trying to send? You can use Apple’s Messages App to send and receive messages between users of other Apple devices.
Do you have an iPhone - or just an iPad? If exchanging messages with Android devices, you’ll need to use SMS/MMS messaging…
An iPad, whether a Cellular model or not, is not capable of directly accessing Cellular Voice or SMS/MMS Messaging features. An iPad with either WiFi or Cellular connectivity alone can only access IP-data services. If you have added a DataSIM and Cellular plan to a WiFi+Cellular model of iPad, the number associated with the SIM card is only used to identify your account for billing purposes. This number is not used for making calls or sending messages.
However, when paired with an iPhone, the capabilities of iPad significantly broaden to include access to Cellular Voice and Messaging services of the associated iPhone - relayed to the iPad over WiFi using Apple’s continuity features.
More information about Continuity and the relevant Cellular services can be found here:
Continuity
Use Continuity to connect your Mac, iPhone, iPad, iPod touch and Apple Watch – Apple Support
SMS/MMS Messaging
How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support
WiFi Calling
Make a call with Wi-Fi Calling – Apple Support
If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID - to send SMS/MMS messages (green bubbles) from your iPad you must explicitly enable Text Message Forwarding for your iPad on your iPhone...
On your iPhone:
Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.
Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:
Settings > [Your Name / AppleID] > Messages - set to ON