CLASS D AIRSPACE AND RWY INCURSION AFTER A NORAC PA28 LOW TIME PVT PLT LANDS WITHOUT CLRNC AT GRI; NE.

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I LANDED AT A CTLED ARPT WITH NO COM WITH TWR. I; AS A SINGLE PLT; HAD CHKED WINDS ALOFT FOR 6000 FT AS WE (MY SAFETY PLT AND PAX OBSERVER AND I) WERE FLYING FROM LNK; LINCOLN; NE; TO KEARNEY. I WAS GOING TO FLY UNDER THE HOOD TO LOG INST TIME. UPON CLBOUT; WE HAD REACHED APPROX 6000 FT AND IT WAS QUITE BUMPY; SO I REQUESTED CLRNC TO 10500 FT TO GET OVER THE TOP OF THE BROKEN CLOUDS; BTWN APPROX 7000-8500 FT. AFTER RECEIVING CLRNC; WE CLBED TO 10500 FT AND I BEGAN FLYING INSTS. THIS WAS MY FIRST TIME IN THIS ACFT FLYING INST. THE ACFT HAS DUAL NAVCOMS AND A DME; BOTH TO THE VERY FAR R SIDE OF THE PANEL. I SET THE NAVS TO KEARNEY AND CONTINUED TO FLY. CHKED AWOS AT KEARNEY AND AFTER FLYING FOR APPROX AN HR AND 10-15 MINS; MY SAFETY PLT ANNOUNCED SHE SAW THE ARPT. BOTH NAVS WERE SAYING IT WAS; IN FACT; DIRECTLY IN FRONT OF ME. WE STARTED OUR DSCNT; AND I WAS STILL UNDER THE HOOD. THE DME WAS ACTING SPORADICALLY AT BEST. PERHAPS THEY ACT THIS WAY REGULARLY OR PERHAPS IT WASN'T RECEIVING A GOOD SIGNAL. I DID REF OUR LOCATION TO HSI (HASTINGS; NE) AND APPEARED TO BE ABOUT RIGHT; BUT NOT EXACTLY. I FELT VERY CONFIDENT IN THE BELIEF THAT MY SAFETY PLT WAS CORRECT AS SHE WAS FROM THE AREA. ANYWAY; I LOOKED AT IT; THERE WERE CERTAIN THINGS THAT I WASN'T INTERPING CORRECTLY. ABOUT 5-10 MI OUT; I PULLED OFF THE HOOD; CALLED STANDARD CALLS AND LANDED. UPON LNDG AND PULLING OFF THE RWY; I DID THINK IT WAS RATHER ODD THAT A CITATION ON BASE FROM THE OTHER DIRECTION HADN'T CALLED IN. TO MY SURPRISE; I DIDN'T REALIZE THAT WE WERE IN GRAND ISLAND TILL WE HAD PULLED OFF THE RWY. I EXITED THE ACFT AND WAS CALLED BY THE TWR AT THE FBO. I EXPLAINED WHAT HAD HAPPENED IN DETAIL AND WAS TOLD I WOULD BE CONTACTED BY THE FSDO OFFICE. I WAS; 3 DAYS LATER ITEMS THAT LED DIRECTLY TO MISTAKE ARE: 1) NOT FAMILIAR ENOUGH WITH ACFT NAV EQUIP AND USE AND LIMITATIONS OF EQUIP. 2) DME NOT WORKING ALL THE TIME. 3) LAYOUT OF NAV EQUIP WAS NOT EASILY READABLE FROM PLT'S LOCATION. 4) LAYOUT OF ARPTS ARE EXACTLY THE SAME.