A FLT CREW TAXIED ACROSS AN ACTIVE RWY AT SFO WITHOUT CLRNC BECAUSE OF LACK OF POSITIONAL AWARENESS.

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I WAS SERVING AS THE SIC IN THE L SEAT ON AN IFR FLT FROM SFO. THE PIC HAD FILED THE FLT PLAN AND WAS IN THE R SEAT. I WAS PERFORMING PAX DUTIES AND WAS NOT IN THE SEAT WHEN THE ATIS AND CLRNC WERE OBTAINED BY THE PIC BUT WAS BRIEFED THAT INFO BY HIM. I STARTED THE R ENG AND ASKED THE R SEAT PLT PIC TO CALL FOR TAXI AS I WAS REVIEWING THE RATHER COMPLICATED SFO DEP PROC WE WERE CLRED TO FLY. I DID NOT FULLY HEAR OR UNDERSTAND THE TAXI INSTRUCTION OVER THE COCKPIT SPEAKER AS I WAS ADDITIONALLY TRANSITIONING TO MY HEADSET BUT UNDERSTOOD THAT WE WOULD HAVE AN INTXN TKOF ON RWY 28R. I FELT CONFIDENT THAT THE R SEAT PIC UNDERSTOOD THE FULL TAXI INSTRUCTIONS SINCE HE HAD ACKNOWLEDGED THE INSTRUCTIONS AND ASSUMED THAT HE HAD PREVIOUSLY REFERRED TO THE TAXI DIAGRAM IN THE BOOK ON HIS SIDE OF THE COCKPIT AND WOULD ADVISE ME OF ANY TAXI DEVS AS IS SOP'S. I PWRED UP THE R ENG AND TAXIED OUT OF THE FBO RAMP. I HAD STARTED ONLY 1 ENG BECAUSE I WAS EXPECTING A LONG TAXI AND POSSIBLE TKOF DELAYS BECAUSE I THOUGHT THE STRONG WESTERLY WINDS I HAD FELT WHILE PREFLTING THE ACFT WOULD CAUSE TOO MUCH XWIND FOR USE OF ANY OTHER RWYS AND IDLE PWR WITH BOTH ENGS RUNNING WOULD CAUSE EXCESSIVE DOWNWIND TAXI SPD. AS I TAXIED EBOUND ON TXWY C; I LOOKED TOWARDS THE DEP END OF RWYS 28R AND 28L AND SAW SEVERAL INTL AIRLINERS WAITING FOR TKOF. MY THOUGHTS WERE THAT WE WOULD BE GIVEN ONE OF THE INTXNS FOR TKOF PRIOR TO THE END OF RWY 28R SO AS TO NOT BE IN THE WAY OF THE AIRLINERS WAITING AT THE END. AS I APCHED RWY 1L AND 1R ON TXWY C; I ASKED THE PIC IN THE R SEAT IF WE WERE CLRED TO CROSS THOSE RWYS. HE TOLD ME THAT WE WERE. I INSTINCTIVELY AND DILIGENTLY LOOKED DOWN BOTH RWYS AND SAW NO ACFT EITHER ON THE RWYS OR APCHING FROM THE AIR. I FELT THAT EVERYTHING SEEMED SAFE AND NORMAL AND CROSSED RWY 1L. SFO GND IMMEDIATELY CALLED US AND ASKED WHAT WE WERE DOING AND NOTIFIED US THAT WE WERE NOT CLRED TO CROSS THAT RWY AND HAD TAXIED PAST OUR INTENDED INTXN FOR DEP WHICH WAS TO BE RWY 28R AT TXWY E. OUR HEARTS SANK WHEN WE BOTH REALIZED THAT WE HAD PROBABLY DONE A RWY INCURSION AND HAD NOT STRICTLY FOLLOWED ATC TAXI INSTRUCTIONS. WE APOLOGIZED FOR OUR MISTAKE BUT WERE ADVISED TO CALL BACK THE TWR ASAP. WE WERE THEN CLRED TO CROSS RWY 1R; STARTED THE OTHER ENG; COMPLETED ALL APPROPRIATE CHKLISTS; CONTACTED TWR AND DEPARTED RWY 28R AT TXWY L. AFTER LNDG AT DEST; WE CALLED THE SFO TWR SUPVR AND THE PIC GAVE HIM WHAT INFO HE REQUESTED. BOTH THE PIC AND MYSELF HAVE DISCUSSED IN DETAIL WHAT WE EACH THOUGHT WERE THE CONTRIBUTING FACTORS FOR OUR MISTAKE AND WHAT WE EACH SHOULD HAVE DONE IN ORDER TO PREVENT IT. WE DID NOT ENGAGE IN THE CLASSIC 'BLAME GAME' BUT RATHER ENGAGED IN CONSTRUCTIVE CRITICISM IN ORDER TO IDENT THE PROBABLE EVENTS WE EACH INDIVIDUALLY AND AS A CREW CONTRIBUTED TO THE RWY INCURSION. I BELIEVE THE RWY INCURSION OCCURRED BECAUSE WE AS A FLT CREW DID NOT FULLY UNDERSTAND THE ATC TAXI CLRNC AND HAD A BREAKDOWN IN BASIC CRM AND SITUATIONAL AWARENESS OF 'WHERE ARE WE AND WHERE ARE WE GOING?' CONTRIBUTING CAUSES ARE: 1) MY ASSUMPTION THAT THE STRONG W WINDS WERE PREVENTING THE USE OF RWYS 1R/L. 2) MY ASSUMPTION THAT WE WOULD BE GIVEN MORE RWY LENGTH AND HAVE A LONGER TAXI. 3) MY MISTAKE THAT AS THE SIC TAXIING I WAS NOT READY TO INDEPENDENTLY HEAR AND VERIFY THE TAXI CLRNC WITH THE TAXI DIAGRAM. 4) MY DISTR OF UNDERSTANDING; SETTING UP AND BRIEFING THE DEP PROC. 5) MY ASKING THE PIC IF WE WERE CLRED TO CROSS RWYS 1R/L RATHER THAN ASKING HIM TO CALL GND AND CONFIRM THAT WE WERE CLRED TO CROSS. DURING OUR COMBINED OVER 55 YRS OF AVIATION EXPERIENCE; NEITHER PLT HAS EVER HAD AN ACFT ACCIDENT; INCIDENT; RWY INCURSION OR FAA VIOLATION. WE BOTH UNDERSTAND THE SERIOUSNESS OF RWY INCURSIONS AND ARE WELL AWARE OF THE EMPHASIS THE FAA AND ITS ATC CTLRS PLACE ON THIS MATTER AS EVIDENCED BY THE WEALTH OF ADVISORY CIRCULARS AND OTHER INFORMATIONAL PAMPHLETS ON THIS SUBJECT. THE CORRECTIVE ACTION THAT WE AS A PROFESSIONAL FLT CREW ARE GOING TO UNDERTAKE INDEPENDENTLYOF WHAT THE FAA MAY DETERMINE ARE THE FOLLOWING: 1) REVIEW; EMPHASIS AND RETRAIN IN CRM AND SOP'S ON PREDEP AND TAXI PROCS. 2) OBTAIN; READ AND DISCUSS AS MUCH AVAILABLE INFO ON RWY INCURSIONS INCLUDING FAA ADVISORY CIRCULARS; PAMPHLETS; NASA CALLBACK RPTS; NTSB ACCIDENT RPTS; ETC. 3) ATTEND A RWY INCURSION COURSE. 4) AT THE NEXT RECURRENT TRAINING COURSE; COORD WITH THE INSTRUCTORS TO EMPHASIZE PREDEP AND TAXI PROCS AT HIGH DENSITY ARPTS AND IF POSSIBLE A SIMULATOR SESSION BASED ON THE DEPICTION OF SAN FRANCISCO INTL ARPT AND A RECREATION OF THIS EVENT.