Ebola is not an airborne virus, so it can only enter the body through a cut on the skin, or through the mucous membranes located in the eyes, nose and mouth.
An Ebola patient who is very sick will secrete fluid in many different ways, and these fluids carry the danger. It is not a problem to be in the same room as an Ebola patient, but it is important to be totally covered (hence the photos you have seen of the full suits that the carers wear).
This is because an Ebola sufferer in the final stages of the disease sheds a large amount of Ebola virus particles within their body fluids, so all it takes is for a drop to land on your skin and you could become infected too.
It is easy to imagine the pain that the carers feel when looking after these people and seeing their suffering. You can imagine them shedding a tear for a dying patient and then wiping the tears from their eyes. Yet if they have cleaned up after that patient, that one automatic reaction could cost their life too because they may be carrying the virus on their skin and then have given it access to the body via the eye.
On a lighter note, spare a thought for footballer Dele Adebola who recently had to publicly deny that he had Ebola due to the way his name sounds!