docs: improve getting started installation docs

documentation/docs/01-introduction/02-getting-started.md

@@ -2,7 +2,11 @@
 title: Getting started
 ---
 
-We recommend using [SvelteKit](../kit), which lets you [build almost anything](../kit/project-types). It's the official application framework from the Svelte team and powered by [Vite](https://vite.dev/). Create a new project with:
+We recommend using [SvelteKit](../kit), which lets you [build almost anything](../kit/project-types). It's the official application framework from the Svelte team and powered by [Vite](https://vite.dev/).
+
+Create a new project with your preferred package manager:
+
+**npm:**
 
 ```sh
 npx sv create myapp
@@ -11,6 +15,35 @@ npm install
 npm run dev
 ```
 
+**yarn:**
+
+```sh
+yarn dlx sv create myapp
+cd myapp
+yarn install
+yarn dev
+```
+
+**pnpm:**
+
+```sh
+pnpm dlx sv create myapp
+cd myapp
+pnpm install
+pnpm dev
+```
+
+**bun:**
+
+```sh
+bunx sv create myapp
+cd myapp
+bun install
+bun dev
+```
+
+See the [CLI docs](../cli) for more information about the `sv` command line tool.
+
 Don't worry if you don't know Svelte yet! You can ignore all the nice features SvelteKit brings on top for now and dive into it later.
 
 ## Alternatives to SvelteKit
@@ -21,12 +54,83 @@ You can also use Svelte directly with Vite by running `npm create vite@latest` a
 
 There are also [plugins for other bundlers](/packages#bundler-plugins), but we recommend Vite.
 
+## Installing Svelte in an existing project
+
+If you have an existing project for example via [Inertia](https://inertiajs.com/) and want to add Svelte to it, you can install Svelte and [vite-plugin-svelte](https://github.com/sveltejs/vite-plugin-svelte) manually.
+
+First, install Svelte and the Vite plugin:
+
+**npm:**
+
+```sh
+npm install --save-dev --save-exact svelte @sveltejs/vite-plugin-svelte
+```
+
+**yarn:**
+
+```sh
+yarn add --dev --exact svelte @sveltejs/vite-plugin-svelte
+```
+
+**pnpm:**
+
+```sh
+pnpm add --save-dev --save-exact svelte @sveltejs/vite-plugin-svelte
+```
+
+**bun:**
+
+```sh
+bun add --dev --exact svelte @sveltejs/vite-plugin-svelte
+```
+
+Then, add the Svelte plugin to your `vite.config.js`:
+
+```js
+import { defineConfig } from 'vite';
+import { svelte } from '@sveltejs/vite-plugin-svelte';
+
+export default defineConfig({
+  plugins: [
+    svelte({
+      /* plugin options */
+    })
+  ]
+});
+```
+
 ## Editor tooling
 
 The Svelte team maintains a [VS Code extension](https://marketplace.visualstudio.com/items?itemName=svelte.svelte-vscode), and there are integrations with various other [editors](https://sveltesociety.dev/collection/editor-support-c85c080efc292a34) and tools as well.
 
-You can also check your code from the command line using [`sv check`](https://github.com/sveltejs/cli).
+You can also check your code from the command line using [`sv check`](https://github.com/sveltejs/cli) to check for Unused CSS
+Svelte A11y hints, JavaScript/TypeScript compiler errors.
+
+Alternatively, you can install `svelte-check` (powers `sv check`) directly:
+
+**npm:**
 
+```sh
+npm install --save-dev --save-exact svelte-check
+```
+
+**yarn:**
+
+```sh
+yarn add --dev --exact svelte-check
+```
+
+**pnpm:**
+
+```sh
+pnpm add --save-dev --save-exact svelte-check
+```
+
+**bun:**
+
+```sh
+bun add --dev --exact svelte-check
+```
 
 ## Getting help