I have basically no idea how I could do this. I think I should use MoveIt!, but there are no specefications on the MoveIt! Homepage for my robot.
The 'beauty' of ROS (or any other similar component based system) is that once components implement a certain interface, you can exploit the power-of-abstraction: motion planning for a Motoman MH5F is not (or rather: should not be) any different as for an ABB IRB 2400 or a Fanuc LR Mate 200iD. The fact that "there are no specefications on the MoveIt! Homepage for my robot" does not matter: they are all serial, 6 axis robots, and all the ROS-Industrial drivers implement the same interfaces to control them (in fact: all MoveIt compatible robots implement the same interface, so they can all be controlled in a similar way).
Could you explain me which packages I may need to install for this [..]
This should not be any different from any other use of MoveIt with a compatible manipulator. You normally require (at least) a driver, a 'robot 3D model' and a MoveIt Configuration package. You already have the motoman_driver package. The motoman_mh5_support package could provide you with the '3D model' (be sure to check the geometry, and the joint and velocity limits. I'm not sure how similar the MH5F is to the MH5).
Unfortunately, a MoveIt Configuration for the MH5(F) has not been made available yet, but it isn't too hard to create one: see the Create a MoveIt Package for an Industrial Robot tutorial for that. First though, be sure to try and ask the people on the ROS-Industrial mailing list, they might already have one.
[..] which kind of message I have to publish whereever? Or is there an example or Tutorial for this?
You already mentioned MoveIt, which is currently the motion planning framework for ROS. As a playing-around and debugging interface, I've always found the RViz MoveIt plugin(s) very nice to work with. For direct API access, you can use the C++ or Python interfaces to the move_group API. Configured correctly, this should allow you to plan complete trajectories for your MH5F (or again: any other MoveIt compatible robot).
All of the above links are from the MoveIt tutorials page, which also lists some more advanced uses of the available functionality.
In addition, you might be interested in the ROS-Industrial Basic Developers' Training Class Curriculum which should cover your questions above.
