How do I access my text messages from my iPhone to my MAC?

Here is how to set up the SMS message sharing between your iPhone and your Mac:

Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support

Here is how to configure and use Continuity for what else it can do:

macOS - Continuity - Apple

While you will be able to share SMS, some of the other Continuity features will not be available on macOS 10.13:

System requirements for Continuity on Mac, iPhone, iPad, and Apple Watch - Apple Support

If that Mac can be upgraded to a newer version (that depends on the model year), consider that upgrade:

How to download and install macOS - Apple Support