What's the best way to juice a pineapple? Should the whole fruit be used or should the core be discarded?  (I'd prefer a method that doesn't require one of those huge electric fruit juicers. The only fruit juicers I have are for oranges and a hand one for lemons.) 
I've never juiced a pineapple, but I have done a watermelon and I've had some success with a food processor and a cheese cloth.  I'd remove the core of the pineapple, because I don't think there's much juice in it.  Remove the skin as well.  Then run the pineapple through the food processor and pour all of the contents into a cheese cloth over a bowl.  Squeeze all the juice you can out of whatever's in the cheese cloth.    If you don't have a food processor, you can maybe use a cheese grater or potato masher instead. 