C182 PLT HAD A RWY INCURSION; ON TAXI OUT; AT MDW.

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I WAS PARKED ON THE TIEDOWNS E OF FBO. I HAD JUST OBTAINED MY IFR CLRNC AND CONTACTED MIDWAY GND FOR TAXI INSTRUCTIONS. I RECEIVED AN INSTRUCTION TO FOLLOW A 'TAILDRAGGER' TO RWY 4L; HOLD SHORT OF RWY 4R. AFTER LOOKING FOR THE TAILDRAGGER I NOTIFIED GND THAT I DIDN'T SEE HIM. GND STATED HE WAS 'LONG GONE' AND THAT I SHOULD TAKE A L ON TXWY F AND THEN TAKE TXWY K. THE CTLR WAS VERY BUSY. WHEN I STARTED TO TAXI I MADE A R TURN ON TXWY K (I SHOULD HAVE TURNED L). JUST AS I STARTED TO TAXI ACROSS RWY 31C; I REALIZED MY MISTAKE. THE GND CTLR THEN INFORMED ME I HAD CROSSED AN ACTIVE RWY. HE PROCEEDED TO TELL ME TO 'CROSS RWY 31C; MAKE A 180 DEGS; AND HOLD SHORT OF RWY 31C.' AFTER APPROX 15 SECONDS; I RECEIVED INSTRUCTION TO TAXI STRAIGHT AHEAD ON TXWY K TO RWY 4L; HOLD SHORT OF RWY 4R. AS I APCHED RWY 4R; I RECEIVED CLRNC TO CROSS RWY 4R. THE REST OF THE FLT WAS COMPLETED WITHOUT INCIDENT. I FEEL SEVERAL FACTORS CONTRIBUTED TO MY CONFUSION IN THIS SIT. FOREMOST; THIS WAS MY FIRST TIME INTO CHICAGO MIDWAY. MY CONFIDENCE LEVEL WAS NORMAL; CONSIDERING MY ARR THE DAY BEFORE WAS UNEVENTFUL. I DID HAVE A TAXI DIAGRAM AVAILABLE AND WAS UTILIZING IT. HOWEVER; AS A SINGLE PLT I WAS DISTR BY HAVING TO DIVIDE MY ATTN INSIDE TO THE DIAGRAM AND OUTSIDE WHILE TAXIING. I ALSO WAS FATIGUED DUE TO LACK OF REST THE PREVIOUS EVENING. LASTLY; SOME OF THE TXWY IDENT SIGNS WERE DIFFICULT TO SEE; ESPECIALLY AT THE INTXN OF TXWYS K AND F DUE TO THE COMPLICATED INTXN GEOMETRY AND CLOSE PROX OF RWY HOLD SHORT SIGNS; ETC. IN THE FUTURE; I PLAN TO REVIEW THE TXWY DIAGRAM IN GREATER DETAIL WHILE THE ACFT IS NOT IN MOTION; BE MORE AGGRESSIVE ABOUT ADMITTING ANY CONFUSION CONCERNING MY LOCATION. I ALSO WILL ENSURE I HAVE RECEIVED APPROPRIATE REST BEFORE OPERATING AT A CONGESTED ARPT SUCH AS MIDWAY. AS A CFI; I TEACH THE USE OF THE CHKLIST FOR RECOGNIZING UNSAFE PHYSICAL AND MENTAL CONDITION; AND I WILL REINFORCE THIS STRATEGY IN MY OWN FLYING.