First you have to create an account on vercel and keep it logged into your default browser. Then install the vercel CLI

shnpm i -g vercel

After installing you have to authenticate youself using the vercel login command, go to your command prompt or terminal and type the vercel login command

sh~ vercel login

Vercel CLI 37.7.1
? Log in to Vercel (Use arrow keys)
> Continue with GitHub
  Continue with GitLab
  Continue with Bitbucket
  Continue with Email
  Continue with SAML Single Sign-On
 ─────────────────────────────────
  Cancel

Here you have to select how you want to login on vercel, if you have your vercel account logged in with github select Continue with GitHub and press Enter

This will then open a link into your browser and automatically log you in using vercel and you will see a message saying Vercel CLI Login Success. Also in your terminal you will see a success message

After that open your project on VSCode or any of your faviourite terminal and run the vercel --prod command

shvercel --prod

Follow this gif

After that you can go to vercel dashboard and you can see your project and also live site link