If you're having foot pain, I would not recommend adding cleats if you are not already using them.

First, make sure you have a decent pedal. Something that to small or weirdly shaped (my brothers bike came with oddly poor pedals for such and expensive bike, it was a Specialized Roubax) can hurt your foot.

Here's an easy suggestion for decent pedals ($36) -

WELLGO Alloy BMX Mountain Bike Pedals Sealed 9/16"
[h=1]http://www.amazon.com/Wellgo-Alloy-Sealed-Mountain-16-Inch/dp/B00E7UZ6I0/ref=sr_1_4?ie=UTF8&qid=1405057353&sr=8-4&keywords=wellgo+bike+pedals[/h]
Shoes, biggest thing is to start fit - my feet used to hurt, then I realized my shoes were to narrow.

If they fit well, get something with a non-compressible sole. Chuck Taylor's work. If you want to spend more, some companies like Five-Ten make specific shoes for biking with flat pedals, here's one of them -

Five Ten Freerider
Five Ten - Freerider - Grey / Black