As quickly as possible!
I know it sounds silly but it is true. Stroke is not something you want to sit around and watch. Time lost is Brain lost!
When dealing with a possible stroke you should attempt to get as much patient history as you can but the vital piece of information that the emergency department is going to want is how long the symptoms have been active. If you can't tell them for certain what the last known normal time was they lose some of their most powerful treatment alternatives.
I typically get a quick set of vitals, start an IV, administer the Stroke Screen questions and then transport code3 to the nearest stroke center so they can get the patient into a CT machine and determine what is really going on. You can't tell the difference between Iscemic and Hemmoragic stroke in the field so there is no point in trying. Avoid dextrose drips unless the pt is currently hypoglycemic. Remember that one set of symptoms can often mask or mimic another. If you have a hypoglycemic diabetic but you never check the sugar you might just misidentify it as an active stroke. Nobody wants to be the guy that called a stroke alert when all he really needed was an amp of D50...