Simple answer. Use the Angular CLI and issue the

ng build 

command in the root directory of your project. The site will be created in the dist directory and you can deploy that to any web server.

This will build for test, if you have production settings in your app you should use

ng build --configuration production

This will build the project in the dist directory and this can be pushed to the server.

Much has happened since I first posted this answer. The CLI is finally at a 1.0.0 so following this guide go upgrade your project should happen before you try to build. https://github.com/angular/angular-cli/wiki/stories-rc-update

You are actually here touching two questions in one.

The first one is How to host your application?.
And as @toskv mentioned its really too broad question to be answered and depends on numerous different things.

The second one is How do you prepare the deployment version of the application?.
You have several options here:

1. Deploy as it is. Just that - no minification, concatenation, name mangling, etc. Transpile all your ts project copy all your resulting js/css/... sources + dependencies to the hosting server and you are good to go.

2. Deploy using special bundling tools, like webpack or systemjs builder.
   They come with all the possibilities that are lacking in #1.
   You can pack all your app code into just a couple of js/css/... files that you reference in your HTML. systemjs builder even allows you to get rid of the need to include systemjs as part of your deployment package.

3. You can use ng deploy as of Angular 8 to deploy your app from your CLI. ng deploy will need to be used in conjunction with your platform of choice (such as @angular/fire). You can check the official docs to see what works best for you here

Yes you will most likely need to deploy systemjs and bunch of other external libraries as part of your package. And yes you will be able to bundle them into just couple of js files you reference from your HTML page.

You do not have to reference all your compiled js files from the page though - systemjs as a module loader will take care of that.

I know it sounds muddy - to help get you started with the #2 here are two really good sample applications:

SystemJS builder: angular2 seed

WebPack: angular2 webpack starter

With the Angular CLI it's easy. An example for Heroku:

1. Create a Heroku account and install the CLI

2. Move the angular-cli dep to the dependencies in package.json (so that it gets installed when you push to Heroku.

3. Add a postinstall script that will run ng build when the code gets pushed to Heroku. Also add a start command for a Node server that will be created in the following step. This will place the static files for the app in a dist directory on the server and start the app afterward.

"scripts": {
  // ...
  "start": "node server.js",
  "postinstall": "ng build --aot -prod"
}

4. Create an Express server to serve the app.

// server.js
const express = require('express');
const app = express();
// Run the app by serving the static files
// in the dist directory
app.use(express.static(__dirname + '/dist'));
// Start the app by listening on the default
// Heroku port
app.listen(process.env.PORT || 8080);

5. Create a Heroku remote and push to depoy the app.

heroku create
git add .
git commit -m "first deploy"
git push heroku master

Here's a quick writeup I did that has more detail, including how to force requests to use HTTPS and how to handle PathLocationStrategy :)