Hi Gail! Here are some great instructions for you. Good luck.
Be careful with the videos on the page Betty suggested. (Not a knock on Betty) Some of the techniques are flat out wrong. Does your drop ceiling cover bare floor joists or a plaster/ drywall ceiling?Either way, you do not want to install something that will go out of style and then have to tear an entire ceiling down or add another complete layer to cover it up. Install 1x3 strapping perpendicular to the floor joists whether bare or drywall/plaster with screws. Then put up your ceiling.
You would need to put a reg sheet rock ceiling up then you could attach the ship lap on that
shiplap does not need a backing material . you can nail it right to the joists . or studs if used as a wall covering . it will not warp or buckle like butt cut boards will. be careful to check for asbestos if your home is very old .
Duane is right if used for walls, but only if your local building code allows it. You do not want to attach a finished ceiling material directly to your your floor joists. There is too much flex and it will eventually crack or spread apart. The other good thing about using strapping is that you create channels you can run wiring through.