PLT OF A PIPER PA28 INADVERTENTLY TAXIED ONTO THE WRONG TXWY WHICH RESULTED IN XING THE ACTIVE RWY AT A LOCATION WHERE THERE WAS NO ATTACHING TXWY.

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I WAS CLRED TO TAXI FROM THE NE CORNER OF FIELD TO RWY 34L AND TO HOLD SHORT AT INTXN 3E. THEN TOLD JUST TO TAXI UNTIL SHORT OF THE TXWY TO MAKE WAY FOR ANOTHER PLANE. AS I ARRIVED AT THE TXWY; I WAS POSITIONED AT INTXN 4E. WAS TOLD CLR TO TAXI ACROSS RWY 34R; HOLD BEFORE RWY 34L. I THOUGHT THAT BECAUSE I WAS AT INTXN 4E THAT THE CTLR NOW WANTED ME TO CROSS AT INTXN 4E. I CROSSED RWY 34R AND HELD SHORT AT RWY 34L. I WAS THEN CLRED TO TAXI ACROSS RWY 34L; BUT SAW NO INTXN IMMEDIATELY ACROSS THE RWY. I SAW 2 NEARBY INTXNS -- ONE TO THE N (WHICH WAS INTXN 3G); AND ONE TO THE S WHICH WAS INTXN 5G. INTXN 5G APPEARED CLOSEST; SO I ZIGZAGGED S ON RWY 34L AND EXITED ON THE W END OF THE FIELD. AS I WAS ZIGZAGGING; CTL ASKED WHAT I WAS DOING; AND I ANSWERED 'XING THE RWY.' CTL IMMEDIATELY INFORMED ME AS TO MY MISTAKE WITH TXWY ASSIGNMENT AND THEN CLRED ME TO TAXI TO RWY 34L. AFTER TALKING WITH 3-4 OTHER GND TFC; HE EXPLAINED TO ME HOW INTXN 3E USED TO BE PART OF THE OLD RWY. HOW I NEEDED TO BE AWARE OF WHERE TXWYS WERE. I TOLD HIM I WOULD FULLY REMEMBER. THIS EVENT COULD HAVE BEEN AVOIDED SEVERAL WAYS: 1) I NEEDED BETTER FAMILIARITY WITH THE TXWYS VIA AN ARPT DIAGRAM WITH ME AS I TAXIED. 2) I SHOULD HAVE QUERIED CTL WHEN HE CLRED ME TO CROSS IF HE INTENDED INTXN 4E OR INTXN 3E AND NOT JUST ASSUME THAT BECAUSE HE CLRED ME AT THE TIME I REACHED INTXN 4E THAT HE THEN INTENDED ME TO CHANGE TO INTXN 4E. 3) INSTEAD OF DECIDING TO USE INTXN 5G ONCE I REALIZED THAT NO INTXN 4G EXISTED; I SHOULD HAVE ASKED FOR DIRECTIONS. 4) ALSO; SINCE VAN NUYS IS MY HOME FIELD; I SHOULD BE CAREFUL NOT TO BECOME LAX IN FAMILIARITY; BUT TO KEEP AN ARPT DIAGRAM OUT FOR REF WHEN USING THE FIELD. 5) I SHOULD READ BACK ALL CLRNC INSTRUCTIONS. IF CLRED WITHOUT RESTATED LOCATION AS TO WHERE TO MOVE FROM; READ BACK THE LAST ASSIGNED INTXN ASSIGNED. EXAMPLE: 'CLRED TO CROSS RWY 34R AT INTXN 3E; HOLD SHORT RWY 34L.'