Hi Kelechi,
It is pretty easy. You will need to create and express.js API with Nodejs and have the Postgreql in it. Then you can create your Vue Apps and connect to the express API. This will help; https://www.youtube.com/playlist?list=PLWKjhJtqVAbnadueQ-C5keMQQiQau_i0D
I used a similar setup but I wouldn't recommend it except if you absolutely must. Use something like NuxtJs.
If you are starting out with Vue.js and Node.js and wanting to avoid creating servers including local ones running Express.js and are willing to explore cloud services for the database, you may want to consider AWS Amplify or Google Cloud with Firebase to build out your application. While there is a learning curve in using additional technologies, the pay off is that there are tutorials, documentation and videos and there is scope for extending your application if you need to later.