RWY INCURSION; UNAUTH RWY OP WHEN A PA28 TRAINING FLT PERFORMS AN UNAUTH; UNCOORDINATED TKOF AT ROC.

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I WAS TAXIING OUT TO RWY 10 AT THE GREATER ROCHESTER ARPT (ROC); ROCHESTER; NY. MY CFI WAS WITH ME TO DO SOME COMMERCIAL MANEUVERS IN A LCL PRACTICE AREA. I WAS ON THE GND FREQ. I WAS GIVEN A CLRNC TO TAXI FROM FBO TO TXWY INTXN D AT TXWY H. I WAS TOLD TO HOLD SHORT THERE AND DO MY RUN-UP THERE. THE RTE WAS VIA G2 TO TXWY E; CROSS RWY 25/7 (CLOSED AT THE TIME) CONTINUE ON TXWY E THEN; MAKE A R ONTO TXWY D AND HOLD AT TXWY H. WHILE TAXIING OUT TO TXWY D AT TXWY H; THE GND CTLR TOLD ME TO STAY ON FREQ WITH HIM AND NOTIFY HIM WHEN MY RUN-UP WAS COMPLETE. THE ARPT CTLRS WERE VERY BUSY. THERE WERE NUMEROUS TXWYS CLOSED. RWY 25/7 WAS THE NORMAL RWY TO USE BUT; WAS CLOSED FOR AN UPCOMING SPECIAL EVENT. SO; THIS TAXI RTE WAS UNUSUAL FOR ME BUT I UNDERSTOOD THE GND CTLR'S INSTRUCTIONS AND FOLLOWED THEM. AFTER COMPLETING MY RUN-UP ON TXWY D AT TXWY H I CALLED THE GND CTLR AS HE REQUESTED. THIS IS HOW THE PROB AROSE. THE GND CTLR CLRED ME TO TAXI VIA TXWY D; CROSS TXWY H TO RWY 10 FOR AN INTXN DEP. I READ BACK THE CLRNC AS I UNDERSTOOD IT; 'ROGER; TAXI TXWY D; CROSS TXWY H; CLRED FOR THE INTXN DEP RWY 10'. NO HOLD SHORT OR CHANGE TO TOWER FREQ INSTRUCTIONS WERE GIVEN. AS I TAXIED TO RWY 10; I STAYED ON THE GND FREQ AS I WAS INSTRUCTED TO DO. MY CFI WAS GIVING ME INSTRUCTIONS FOR A SOFT FIELD TKOF AND SETTING THE FLAPS FOR ME. AS I PULLED UP TO THE RWY I CHKED L AND R FOR TFC. I SAW NO TFC. MY CFI ASKED IF WE WERE CLRED FOR DEP AND I SAID YES. IT WAS MY UNDERSTANDING THAT WE WERE CLRED TO DEPART ON RWY 10 FROM THE TXWY D INTXN. AS I PULLED OUT ONTO THE RWY I THOUGHT IT WAS ODD THAT I WAS STILL ON THE GND FREQ BUT; HE DID TELL ME TO STAY ON THAT FREQ WITH HIM. I KNOW AT TIMES THEY RUN BOTH TWR AND GND OPS ON THE SAME FREQ. I LINED UP ON THE CTRLINE FOR A SOFT FIELD TKOF; AS I WAS INSTRUCTED TO DO BY MY CFI; AND APPLIED FULL PWR WITHOUT STOPPING. WE TOOK OFF WITH NO PROBS. THEN; THE GND CTLR ADVISED US THAT WE HAD JUST COMMITTED A RWY INCURSION AND THAT WE HAD NOT BEEN CLRED TO TAXI ONTO THE RWY AND TAKE OFF. FURTHERMORE; THAT A BARON WAS ON A 1 MI FINAL APCH AT THE TIME. WE WERE ALLOWED TO GO OUT TO THE PRACTICE AREA BUT; GIVEN INSTRUCTION TO CALL THE ROCHESTER TWR ON OUR RETURN. SOME OF THE CONTRIBUTING FACTORS TO THIS EVENT WERE: A BUSY ARPT WITH SEVERAL CLOSED TXWYS AND A RWY CLOSED; POOR USE OF LANGUAGE AND COM BTWN MYSELF AND THE GND CTLR. UNFAMILIAR TXWYS AND DEP PROCS; MISUNDERSTOOD TAXI INSTRUCTIONS. THE GND CTLR DID NOT CATCH THE ERROR IN MY READBACK; WHEN I STATED THAT I WAS CLRED TO DEPART ON RWY 10. COM WAS THE WEAK LINK IN THIS CHAIN OF EVENTS. CORRECTIVE ACTIONS. IN MY OPINION THIS RWY INCURSION COULD HAVE BEEN PREVENTED IF THE GND CTLR HAD ISSUED A HOLD SHORT INSTRUCTION AND NOT MADE THE ASSUMPTION THAT I WOULD HOLD SHORT OF THE RWY. I MISUNDERSTOOD THE INSTRUCTIONS. MY READBACK TO THE GND CTLR SHOULD HAVE BEEN MORE PRECISE. ADDITIONALLY; I REGRET MY FAILURE TO QUESTION ATC ABOUT REMAINING ON THE GND FREQ WHILE TAXIING TO THE RWY. OTHER FACTORS AFFECTING THE QUALITY OF MY PERFORMANCE WERE FLYING AFTER A LONG WORK DAY. PRIOR TO MY SCHEDULED FLT LESSON; I HAD WORKED A FULL 9 HR DAY; MOST OF IT OUTDOORS IN THE HOT HUMID WX.