Most pallets are nailed together with ringshank nails that are very difficult to pull. Instead of trying to pull the nails out, I recommend cutting the nails. Use a metal blade on a reciprocating saw.
Cut the nails between the boards, keeping the fence on your reciprocating saw flush with the pallet, with the pallet secured in place.
Layout six pallet boards of equal length on a work surface. Adjust so boards are square.
Measure the width of the six pallet boards and cut five 1x2 boards to this length. Also cut 2 scrap boards 6” in length.
Using the 6” spacer wood pieces, attach one 1x2 6” from bottom of the pallet board edge with 1-1/4” nails or staples.
Continue attaching 1x2 boards to the pallet boards, two fasteners per overlap of boards, using the spacers as a guide.
NOTE: Some of the boards are shorter because I was using scrap pieces of wood. I later filled in the short pieces with scrap 1x2s.
Cut 1x2 boards to the length of the pallet boards. Nail or staple to the pallet boards and 1x2 front pieces with 1-1/4” fasteners, edges flush on back and ends.
Repeat steps on top and bottom, cutting a 1x2 board to fit, to complete outer frame.
Sand and finish if desired. I lightly sanded rough areas but decided to keep a natural finish.
Attach chalkboard sticker labels to 1x2 boards, centering on the pallet board behind the 1x2.
Use a hammer to pound small nails into the pallet boards about ½”.
Hang with screws directly through pallet boards into studs in the wall.