Alright, first things first, we need to get the right packages installed. We're talking about "supabase-js" for Supabase, "graphql-yoga" for GraphQL Yoga, and "nodemon" to keep things running smoothly by restarting your node app whenever you make changes.

npm install @supabase/supabase-js graphql-yoga nodemon

Next up, let's create a new project in Supabase. Log in to your Supabase account, click on "New Project", pick a name, and set your database password. Once that's done, head over to the "API" section in your Supabase dashboard. Jot down those URLs and API keys—they're super important for setting up your Supabase client.

Now, let's get our Yoga server up and running. We'll use the "GraphQLServer" from the "graphql-yoga" package. You'll need to define your typeDefs and resolvers. In the file where you're setting up your server, import "GraphQLServer" from "graphql-yoga".

const typeDefs = `
  type Query {
    hello(name: String): String!
  }
`;

const resolvers = {
  Query: {
    hello: (_, { name }) => `Hello ${name || 'World'}`,
  },
};

const server = new GraphQLServer({ typeDefs, resolvers });

server.start(() => console.log('Server is running on localhost:4000'));

Alright, time to connect to your Supabase project. In your main node.js file, import "createClient" from the "supabase-js" package. Use this method along with the Supabase URL and key you noted earlier to connect to your project.

const { createClient } = require('@supabase/supabase-js');

const supabaseUrl = "https://xyzcompany.supabase.co";
const supabaseKey = process.env.SUPABASE_KEY;
const supabase = createClient(supabaseUrl, supabaseKey);

Now that your Supabase client is connected, you can use it in your GraphQL resolvers. For instance, if you want to fetch a list of posts from your Supabase database, your resolver might look something like this:

const resolvers = {
  Query: {
    posts: async () => {
      let { data: posts, error } = await supabase
        .from('posts')
        .select('*');
      if (error) console.log(error);
      return posts;
    },
  },
};

In this query, we're using the "from()" function to specify the table name (posts) and the "select()" function to fetch all columns (*) from our Supabase Postgres database.

By integrating Supabase into your GraphQL Yoga application's resolvers, you can easily interact with your Postgres database.