How to....Make a shelf from a pallet??

Oh dear. Can you see how the slats have been attached to the playwood Tami?

You usually use a saw and cut the pieces off next to the cross piece where they are attached using a sawzaw or a circular saw.

Tearing it apart in a manner to save the wood is the most difficult. Type into Google: Building with Pallets. Lots of nifty stuff can be made and I love getting them with a cover of Plywood. That cover can be used for so many more things. Go to a site called Instructables and use their search engine. All kinds of goodies there.

Actually a flat crowbar/wrecking bar, a hammer and an extra block of wood helps. Use the flat bar close to the nails putting the pallet together and pound in as far as possible with the hammer. pry upwards untill the nail heads, one or two of them, rise a little when you pound the board back down. Lay your block of wood as close to nails as possible. put claw hammer on block and try prying yp the nails. if they move at all pry again. Turn hammer side ways on block and bend nails ove side ways toward block. This gives you more leverage on the nails, and block of wood causes less damage to the slat it is on. Then you just have to keep working at it in this manner until those twist screw like nails turn loose and come out. Then you have longer pieces of wood and can plug and finish the holes.

You got this https://www.youtube.com/watch?v=YiZaD3tXTSw