SMA CROSSED AN ACTIVE RWY WITHOUT ATC AUTHORIZATION.

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TAXI INSTRUCTIONS: CAT CROSS 21L; W TO P. I TAXIED FROM THE S TEE HANGARS ON TAXIWAY CAT; ACROSS RWY 21L; ONTO TAXIWAY W. THEN AT TAXIWAY ARC AND W; I COULDN'T FIND TAXIWAY P. AT THIS POINT; I ASKED FOR PROGRESSIVE FOLLOWING AND I WAS TOLD THAT I HAD PASSED IT AND TO GO TO TAXIWAY V. AT THIS POINT; I WAS CONFUSED AS TO WHERE I WAS ON THE TAXIWAY. I MADE A L TURN THINKING I WAS STILL ON TAXIWAY W AND I WAS LOOKING FOR TAXIWAY V. I THINK DETROIT METRO GND KNEW I WAS CONFUSED AND SHOULD HAVE BEEN MORE HELPFUL IN GIVING ME DIRECTIONS. SHORTLY AFTER RECEIVING THE LAST TAXI INSTRUCTIONS; I WAS ADVISED THAT I HAD CROSSED THE ACTIVE RWY; AND DIRECTED TO MAKE A 180 AND HOLD. GND ASKED ME IF I COULD ACCEPT AN INTXN TKOF TO WHICH I REPLIED YES. THEN I WAS TOLD TO CONTACT THE TWR SUPVR AFTER LNDG AT MY DEST. I CALLED UPON ARR AT SPRINGFIELD; OH; AND I WAS TOLD THAT THEY WERE FORWARDING THIS INCIDENT TO THE FLT STANDARDS OFFICE. AT THE TIME OF THIS INCIDENT; THERE WAS NO INCOMING OR OUTGOING TFC ON 21C. THE DEPICTION OF TAXIWAYS ON THE PLATES SHOWS A RTE FROM TAXIWAY W TO P VIA TAXIWAY ARC. THIS IS NOT SHOWN ON THE NOS PLATES I USE; NOR WAS IT INCLUDED IN THE CTLR'S TAXI INSTRUCTIONS. A COPY OF THE PLATES ARE ENCLOSED. I FEEL: 1) I WAS GIVEN BAD TAXI INSTRUCTIONS BY METRO GND. 2) ARPT TAXIWAY SIGNS ARE CONFUSING AT DETROIT METRO. 3) I WAS NOT GIVEN PROPER PROGRESSIVE FOLLOWING BY DETROIT METRO GND.