my 2008 4 cyl Chevrolet Malibu has no transmission fluid dip stick how can i check it myself?

Many vehicles do not have dip sticks for their transmissions these days, as they use longer lasting fluids that don't dissipate or require changing for 100K or so. Your shifting issue could be caused by a sensor in either the engine or transmission, and since everything is electronically controlled, your best option is to have a diagnostic scan done to see if any trouble codes appear. That being said, your 08 Malibu has a 5 yr 100 miles warranty on the drivetrain, so depending one when it was put into service your drivetrain (engine & transmission etc.)is still covered under the factory warranty. A quick call to any Chevy dealer service dept. with your VIN # will give you that answer, and if still covered the diagnoses and or repair will be covered.