Often the fastest way to evolve Pokemon is fast training. either buy an action replay, or pit your Pokemon against foes 25% higher lvl that you're supereffective against. So for a Pokemon like mareep/flaaffy/ampharos, attack water and flying types.
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You give on of your Pokemon the soothe bell and it will get happy faster.(It helped me evolve my eevee and togepi.)
Evee is the most common. She can use any stone to evolve. Keep in mind that when you evolve a Pokemon it doesn't learn moves quickly, but if you keep it from evolving it will learn moves faster. You can, however, make it learn moves fast then evolve it, or evolve it then make it use TMs.
There is not really a easiest pokemon to evolve...but bug type pokemon evolve really fast
Tynamo will evolve into Elektrik will evolve into Elektross with a thunderstone in Pokemon White.
Emolga does not evolve. I played Pokemon White also and it does not evolve. Some Pokemon do but this one does not evolve.