Here's an example:
string url = "
http://VaultServer/VaultService";
string username = "username";
string password = "username";
string repository = "Repository Name";
// Set the login options and login/connect to a repository.
ServerOperations.client.LoginOptions.URL = url;
ServerOperations.client.LoginOptions.User = username;
ServerOperations.client.LoginOptions.Password = password;
ServerOperations.client.LoginOptions.Repository = repository;
ServerOperations.Login();
ServerOperations.client.ClientInstance.Connection.InitDragnetService();
MantisItem mi = new MantisItem();
mi.ProjectID = 102; // your project id here
mi.Description = "Some description";
mi.TypeID = (int) ItemTypeVal.Bug;
mi.Details = "Some details";
mi.PlatformID = (int) PlatformVal.Windows;
ServerOperations.client.ClientInstance.Connection.DragnetServiceInstance.AddItemExternal(mi);