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Check-out for edit an item in TFS programmatically
var workspaceInfo = Workstation.Current.GetLocalWorkspaceInfo(fileName);
var server = new TfsTeamProjectCollection(workspaceInfo.ServerUri);
var workspace = workspaceInfo.GetWorkspace(server);

workspace.PendEdit(fileName);

workspace.PendEdit(fileName);

var registerdCollection = RegisteredTfsConnections.GetProjectCollections().First();
var projectCollection = TfsTeamProjectCollectionFactory.GetTeamProjectCollection(registerdCollection);
var versionControl = projectCollection.GetService<VersionControlServer>();

var workspaceInfo = Workstation.Current.GetLocalWorkspaceInfo(_fileName);
var server = new TeamFoundationServer(workspaceInfo.ServerUri.ToString());
var workspace = workspaceInfo.GetWorkspace(server);

workspace.PendEdit(fileName);

var workspaceInfo = Workstation.Current.GetLocalWorkspaceInfo(fileName);
var server = new TfsConfigurationServer(workspaceInfo.ServerUri);
var workspace = workspaceInfo.GetWorkspace(server.GetTeamProjectCollection(workspaceInfo.ServerGuid));

workspace.PendEdit(fileName);

var tfs = new TeamFoundationServer("http://server:8080/tfs/collection");
var version = (VersionControlServer)tfs.GetService(typeof(VersionControlServer));
var workspace = version.GetWorkspace("WORKSPACE-NAME", version.AuthorizedUser);

workspace.PendEdit(fileName);