Deployment from GitHub into Vercel is super duper eazy.
Step 1: Prepare Your Next.js Project
Make sure your Next.js project is ready for deployment.
1.1 Initialize a Next.js app (if you haven't already):
npx create-next-app@latest my-next-app
cd my-next-app
1.2 Build your application locally (optional): It's a good idea to ensure everything is working before deploying:
npm run dev
Step 2: Set Up a Vercel Account
Create a Vercel Account: If you don’t have a Vercel account.
you can sign up at https://vercel.com/signup.
Step 3: Setup Project
choose Project from Add New drop down.

Step 4: Adjust Github App Permission
Adjust Github App Permission or choose existing one.
I believe we have to link with our github account for the first time.

Step 5: Modify Environment Variable

then click Deploy
we perhaps need to wait a moment.

We will see our home page of the app with the Congratulations message like the following img.

click Continue to Dashboard button.
Deployment is done. so we can visit to our site that provided by Vercel.
https://search-pokemon-wwpj-evskfvo3h-applixs-projects.vercel.app/

Step 6: Domain Setup
click the domains from above picture then we will reach to the following page.
click edit


hit the "add"
We will have ip of the our app.
copy ip and point it from your hosting.

we can say it is done.
if you wish to enable name server on vercel. you can.
for more information please visit to there https://vercel.com/docs/projects/domains/add-a-domain