This tutorial uses this repo as a starting point:
https://github.com/andrewdownie/standalone-serverless-backend-using-netlify-lambda

This tutorial is a part of this series:
https://github.com/andrewdownie/netlify-series

1) Get a faunadb secret key and save the key into your netlify environment variables

https://github.com/netlify/netlify-faunadb-example#2-setup-faunadb
The above tutorials pictures are out of date, but it's easy enough to follow along with just the description.

In the linked tutorial you will created a faunadb database, generate an access key to that database, and then save your key to a variable with the name of FAUNADB_SERVER_SECRET in your netlify project.

This variable will get pulled in during the netlify build, and we will reference it in step 5 using process.env.FAUNADB_SERVER_SECRET.

2) In the root folder of standalone-serverless-backend-using-netlify-lambda, install the faunadb package:

npm i faunadb

3) In the root folder, create a file named webpack.config.js, and file it with the following:

This will fix an import error caused by the netlify-lambda package when trying to import node modules The mode: "development" is optional, and will prevent the resulting JS from being uglified, which is needed for debugging code issues

var webpack = require('webpack');

module.exports = {
    plugins: [
        new webpack.DefinePlugin({"global.GENTLY": false})
    ],
    node: {
        __dirname: true
    },
    mode: "development"
};

4) Modify the start and build scripts in the package.json file to reference the webpack.config.js file you just created:

Just add -c ./webpack.config.js to the end of each script command

"scripts": {
  ...
  "start": "netlify-lambda serve src -c ./webpack.config.js",
  "build": "netlify-lambda build src -c ./webpack.config.js"
  ...
}

5) Create a new file in the src folder called 'createDB.js', fill it with the following:

Fun fact: if you don't setup an entry in indexes, you will be able to add items to your faunadb class no problem, but you wan't be able to see them unless you know their faunadb id. Creation of indexes entry is recommended unless you have a reason not to.

import faunadb from 'faunadb';
const q = faunadb.query;

exports.handler = (event, context, callback) => {
    const client = new faunadb.Client({
        secret: process.env.FAUNADB_SERVER_SECRET
    })

    // create the class Messages
    client.query(q.Create(q.Ref('classes'), {name: 'Messages'}))
    .then(() => {
    
        // create an index so we can look at the contents of the Messages class
        client.query(q.Create(q.Ref('indexes'), {
            name: 'all_messages',
            source: q.Ref('classes/Messages')
        }))
        .then(() => {
            callback(null, {
                statusCode: 200,
                body: 'database meow',
                headers: {
                    'Access-Control-Allow-Origin': '*'
                }
            })
        })
    })
    
};
 

6) Open your faunadb in the faunadb web UI to confirm that the Message class and the index have been created

adding items to the Messages class is as follows: client.query(q.Create(q.Ref('classes/Messages'), {data: {exampleKey: 'example value'} }))

Put into words: the second parameter of q.Create takes an object with a data propety, where the value of this data property is itself an object that has the data you want to put into the database.

"errorMessage":"n is not a function"

This error is caused by your webpack.config.js not properly being added to your start/build commands. Check for that step 4 was done correctly and that there are no typos in your webpack.config.js file. If your webpack.config.js worked properly you would get a more meaningful error message due to the mode: "development"