Open the existing sink tray and empty the contents. Set the items inside on the counter top or put them in the dishwasher to wash.
Locate the mounting hinges on either side of the tray. These may be scissor hinges or tilt hinges.
Hold the tray door open with one hand and unfasten the retaining screws on the mounting hinge on one side of the tray. Put the screws and hinge in a sandwich bag to reuse in the future.
Continue to hold the sink tray door open and unfasten the retaining screws on the other side, freeing the hinge from the cabinet frame. Put the hinge and screws into the sandwich bag as well, then set the old sink tray aside.
Tightly roll up a few pages of newspaper. Open the hinge on the new sink tray and wedge the rolled newspaper into the pivot of the hinge to hold it open. Hold the replacement tray up to the recess and drive the retaining screws that came with the replacement tray through the hinge hole and into the cabinet frame using a screw gun.
Roll up more pages of newspaper tightly and wedge it into the hinge's pivot to hold the hinge open. Drive the retaining screws through the hinge holes and into the cabinet frame with the screw gun.
Remove the newspaper on either side and use your kitchen sink tray as normal.