Update and cleanup README (#63)

* Update checkout action version

README.md

@@ -2,10 +2,13 @@
 
 [![Dart](https://github.com/dart-lang/setup-dart/workflows/Dart/badge.svg)](https://github.com/dart-lang/setup-dart/actions?query=workflow%3A%22Dart%22+branch%3Amain)
 
-This [GitHub Action](https://github.com/dart-lang/setup-dart) installs and sets up of a Dart SDK for use in actions by:
+This [GitHub Action](https://github.com/dart-lang/setup-dart) installs 
+and sets up of a Dart SDK for use in actions by:
 
 * Downloading the Dart SDK
-* Adding the [`dart`](https://dart.dev/tools/dart-tool) command and `pub` cache to path
+* Adding the [`dart`](https://dart.dev/tools/dart-tool) command 
+  and [`pub` cache](https://dart.dev/tools/pub/cmd/pub-get#the-system-package-cache)
+  to the system path
 
 # Usage
 
@@ -16,19 +19,20 @@ The action takes the following inputs:
   * `sdk`: Which SDK version to setup. Can be specified using one of two forms:
     * A specific SDK version, e.g. `2.7.2` or `2.12.0-1.4.beta`
     * A release channel, which will install the latest build from that channel.
-      Available channels are `stable`, `beta`, `dev`, and `main`. See
-      https://dart.dev/tools/sdk/archive for details.
+      Available channels are `stable`, `beta`, `dev`, and `main`. 
+      See the [Dart SDK archive](https://dart.dev/get-dart/archive) for details.
 
   * `flavor`: Which build flavor to setup.
-    * Avaliable build flavors are `raw` and `release`.
+    * Available build flavors are `raw` and `release`.
     * `release` flavor contains published builds.
     * `raw` flavor contains unpublished builds, which can be used by developers
       to test against SDK versions before a release.
     * `main` release channel only supports `raw` build flavor.
 
   * `architecture`: The CPU architecture to setup support for. Valid options are
     `x64`, `ia32`, `arm`, and `arm64`. Note that not all CPU architectures are
-    supported on all operating systems; see https://dart.dev/tools/sdk/archive
+    supported on all operating systems; see the 
+    [Dart system requirements](https://dart.dev/get-dart#system-requirements)
     for valid combinations.
 
 ## Basic example
@@ -40,23 +44,23 @@ name: Dart
 
 on:
   push:
-    branches: [ master ]
+    branches: [ main ]
   pull_request:
-    branches: [ master ]
+    branches: [ main ]
 
 jobs:
   build:
     runs-on: ubuntu-latest
 
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: dart-lang/setup-dart@v1.3
 
       - name: Install dependencies
         run: dart pub get
 
       - name: Hello world
-        run: dart bin/hello_world.dart
+        run: dart run bin/hello_world.dart
 ```
 
 ## Check static analysis, formatting, and test example
@@ -111,7 +115,7 @@ jobs:
         os: [ubuntu-latest, macos-latest, windows-latest]
         sdk: [stable, beta, dev, 2.10.3, 2.12.0-29.10.beta]
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: dart-lang/setup-dart@v1.3
         with:
           sdk: ${{ matrix.sdk }}
@@ -125,7 +129,7 @@ jobs:
 
 ## Testing older Dart SDKs example
 
-The Dart SDK continously evolves, and new features and tools are added. The Dart
+The Dart SDK continuously evolves, and new features and tools are added. The Dart
 2.10 SDK introduced a new unified `dart` developer tool, which is what we use in
 the usage examples above for installing dependencies, verifying formatting,
 analyzing, etc. If you need to test a combination of SDKs before and after Dart
@@ -140,7 +144,7 @@ jobs:
         os: [ubuntu-latest, macos-latest, windows-latest]
         sdk: [stable, beta, dev]
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: dart-lang/setup-dart@v1.3
         with:
           sdk: ${{ matrix.sdk }}
@@ -160,7 +164,7 @@ jobs:
         os: [ubuntu-latest, macos-latest, windows-latest]
         sdk: [2.9.0, 2.8.1]
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
       - uses: dart-lang/setup-dart@v1.3
         with:
           sdk: ${{ matrix.sdk }}
@@ -181,8 +185,8 @@ jobs:
     in an environment variable, `DART_HOME`
     ([#43](https://github.com/dart-lang/setup-dart/issues/43))
 
-  * Fixed a issue where cached downloads could lead to unzip issues
-    on self hosted runners
+  * Fixed an issue where cached downloads could lead to unzip issues
+    on self-hosted runners
     ([#35](https://github.com/dart-lang/setup-dart/issues/35))
 
 ## v1.2