Open a window so you get adequate ventilation.
Remove the hardware on the cabinets and unscrew the doors. Set the doors on newspaper. Remove the hinges from the doors or inset cabinet.
Sand the cabinets and the doors with the fine sandpaper to open the grain so it will accept the stain. Oak is a hard wood and needs to have some friction to expand the wood fibers. Vacuum up the dust, then wipe down all the wood surfaces with a rag dipped in mineral spirits. This will clean the wood, and it will dry in no time.
Tape around the cabinets and any areas that abut the wood that is to be stained. Press the tape down all around firmly so there are no leaks. Put newspaper or tarp under the hanging inset part of the cabinets.
Soak the applicator or sponge brush with oak stain and apply it in the direction of the grain. Let it soak in; repeat if you have missed a spot. The stain is quite thin, so be careful as it may drip or spatter. You can also apply the stain using the rags soaked in oak stain and rubbing across the wood surface. Wipe with a clean rag to remove any excess stain.
Wait 24 hours, then turn over the cabinet doors and stain them. Wait 24 more hours, then apply a clear protectant or wax. Let that dry for at least 12 hours, then coat the other side. Reattach the hinges and hardware, and put the cabinet doors back on the insets.