One way is to boil them in water until they are almost fully cooked. Probably 20 minutes or so if they are whole.
Then let them cool or refrigerate them in a covered dish or plastic bag.
Slice the potatoes into rounds about an 1/8-1/4 inch thick. (edit- or cubes if you prefer)
Heat up some butter and/or oil and brown the sliced potatoes in it.
Or you could shred the raw potatoes, if you have something to shred them with.
Then fry the raw shredded potatoes.
For storing the raw potatoes, the tip above about keeping them in water with some lemon is a good one. But they ought to keep in plain water overnight I think.