How do I implement secure OAuth2 consumption in Javascript?

The Implicit Grant flow (the one you’re referring to as User-Agent Flow) is exactly the way to go:

The implicit grant is a simplified authorization code flow optimized for clients implemented in a browser using a scripting language such as JavaScript.

To understand the flow, the documentation from Google for client-side applications is a really good place to start. Note that they recommend you to take an additional token validation step to avoid confused deputy problems.

Here is a short example implementation of the flow using the Soundcloud API and jQuery, taken from this answer:

<script type="text/javascript" charset="utf-8">
  $(function () {
    var extractToken = function(hash) {
      var match = hash.match(/access_token=([\w-]+)/);
      return !!match && match[1];
    };

    var CLIENT_ID = YOUR_CLIENT_ID;
    var AUTHORIZATION_ENDPOINT = "https://soundcloud.com/connect";
    var RESOURCE_ENDPOINT = "https://api.soundcloud.com/me";

    var token = extractToken(document.location.hash);
    if (token) {
      $('div.authenticated').show();

      $('span.token').text(token);

      $.ajax({
          url: RESOURCE_ENDPOINT
        , beforeSend: function (xhr) {
            xhr.setRequestHeader('Authorization', "OAuth " + token);
            xhr.setRequestHeader('Accept',        "application/json");
          }
        , success: function (response) {
            var container = $('span.user');
            if (response) {
              container.text(response.username);
            } else {
              container.text("An error occurred.");
            }
          }
      });
    } else {
      $('div.authenticate').show();

      var authUrl = AUTHORIZATION_ENDPOINT + 
        "?response_type=token" +
        "&client_id="    + clientId +
        "&redirect_uri=" + window.location;

      $("a.connect").attr("href", authUrl);
    }
  });
</script>
<style>
  .hidden {
    display: none;
  }
</style>

<div class="authenticate hidden">
  <a class="connect" href="">Connect</a>
</div>

<div class="authenticated hidden">
  <p>
    You are using token
    <span class="token">[no token]</span>.
  </p>

  <p>
    Your SoundCloud username is
    <span class="user">[no username]</span>.
  </p>
</div>

For sending XMLHttpRequests (what the ajax() function does in jQuery) using AngularJS, refer to their documentation of the $http service.

If you want to preserve state, when sending the user to the authorization endpoint, check out the state parameter.