PA28 INSTRUCTOR AND STUDENT MADE AN APCH TO THE WRONG ARPT. PLTS ENTERED CLASS D WITHOUT CLRNC.

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ENRTE TO X07 FROM SEF. DIVERSION EXERCISE TO GIF. MISNAVIGATION ON DIVERSION; ENDED UP WELL OFF COURSE. SAW LAL; LOOKED TO BE GIF (SIMILAR CONFIG; ETC). ENTERED TFC PATTERN; DSCNDED UNTIL MY NUMBERS WERE IN SIGHT. EXECUTED GAR WHEN DETERMINED IT WAS THE WRONG ARPT. CONTACTED LAL TWR AND ADVISED OF OUR LOCATION AND INTENTIONS. ON SHORT FINAL; LIGHTS WENT OUT; AND TURNED BACK ON AFTER CLICKING MICROPHONE; ENSURING PLTS THAT THEY WERE AT THE CORRECT LOCATION. THE PROB AROSE DURING A TRAINING CROSS-COUNTRY FLT FROM MLB-SUA-SEF-X07-MLB. MY INSTRUCTOR DIVERTED ME TO WINTER HAVEN ARPT HALFWAY BETWEEN SEF AND X07. I MUST HAVE MISCALCULATED THE DISTANCE BECAUSE I ENDED UP OVER LAKE. MY INSTRUCTOR CONSULTED TO THE MAP AND SAW AN ARPT OFF IN THE DISTANCE. HE THOUGHT IT WAS WINTER HAVEN SO WE HEADED TOWARD IT. GETTING CLOSER WE BOTH REALIZED IT WASN'T WINTER HAVEN EITHER. SO MY INSTRUCTOR RE-CONSULTED TO THE MAP AND WE CIRCLED FOR A MIN TO TRY AND RE-ORIENT OURSELVES. USING PILOTAGE MY INSTRUCTOR GUIDED ME TO ONE MORE ARPT. THE RWY CONFIG WAS SIMILAR TO WINTER HAVEN AND HE WAS ALMOST SURE IT WAS THE RIGHT ARPT. WE THEN PROCEED TO MAKE TFC RPTS AND START THE APCH. TO MAKE SURE IT WAS WINTER HAVEN MY INSTRUCTOR USED THE MIKE TO BRIGHTEN THE RWY LIGHTS. AT THE SAME TIME THE TWR BRIGHTENED THE LIGHTS MAKING US THINK IT WAS THE RIGHT ARPT. SO WE PROCEED WITH CAUTION. WHEN WE WERE ABOUT 500 FT ABOVE THE RWY MY INSTRUCTOR QUICKLY REACTED WHEN HE SAW THAT THE RWY NUMBER WAS INCORRECT AND INSTRUCTED ME TO GAR. AT THAT MOMENT THE TWR FOUND THE FREQ WE WERE ON AND CONTACTED US. HE MADE US AWARE OF THE SIT AND MY INSTRUCTOR LET HIM KNOW THAT WE REALIZED WHAT HAD HAPPENED. WE NAVIGATED BACK TO MLB AND CALLED LAKELAND TWR. IN THE FUTURE I WILL ALWAYS USE VOR NAVIGATION IF AVAILABLE AND IF I DOUBT MY POS I WILL CONTACT APCH OR CENTER AND VERIFY IT WITH THEM BEFORE PROCEEDING TO MAKE AN APCH.