public VersionManager GetVersionManager()

public Geodatabase ConnectToVersion(Geodatabase geodatabase, string versionName)
{
  Geodatabase connectedVersion = null;

  if (geodatabase.IsVersioningSupported())
  {
    using (VersionManager versionManager = geodatabase.GetVersionManager())
    using (Version version = versionManager.GetVersion(versionName))
    {
      connectedVersion = version.Connect();
    }
  }
  return connectedVersion;
}

public async Task WorkingWithVersions()
{
  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    using (Geodatabase geodatabase = new Geodatabase(new DatabaseConnectionFile(new Uri("path\\to\\sde\\file"))))
    using (VersionManager versionManager = geodatabase.GetVersionManager())
    {
      IReadOnlyList<Version> versionList = versionManager.GetVersions();

      //The default version will have a null Parent
      Version defaultVersion = versionList.First(version => version.GetParent() == null);

      IEnumerable<Version> publicVersions = versionList.Where(
        version => version.GetAccessType() == VersionAccessType.Public);
      Version qaVersion = defaultVersion.GetChildren().First(
        version => version.GetName().Contains("QA"));

      Geodatabase qaVersionGeodatabase = qaVersion.Connect();

      FeatureClass currentFeatureClass = geodatabase.OpenDataset<FeatureClass>("featureClassName");
      FeatureClass qaFeatureClass = qaVersionGeodatabase.OpenDataset<FeatureClass>("featureClassName");
    }
  });
}