Meticulousness is key
This is Personal Protective Equipment Level C: three pairs of gloves, protective layers, a lot of duct tape, and a respirator. Here's how you take them off safely:
This is one of those things where each individual part of the procedure is straightforward, but even a small mistake can result in disaster. Success depends on following the rules with extreme anal-retentiveness. Preventing infections from IVs and catheters is similarly exacting, and Atul Gawunde has written brilliantly about how a simple checklist has shown great promise in cutting hospital infections.
I should note there is some dispute about what level of protection Ebola health care workers should use. In particular, most pictures I've seen of health care workers in the field have not included the respirator. U.S. hospitals are reportedly tightening up their procedures.