to help here is the normal sequence of operation for a 80% natural gas furnace built in the last 10-15 or so years
T-stat sees a need for heat by temperature set by user...
T-stat calls for heat
inducer motor starts and pulls negative pressure on heat exchanger as it vents out the flue
pressure switch sees negative pressure and allows igniter to glow or spark
once igniter is sparking or glowing the board then sends power to the gas valve
the gas valve opens and lights off the igniter.
the flame sensor then confirms the gas lit and is burning
for around 20-90 seconds the unit warms the heat exchanger
then the board calls for indoor fan motor to come on and blow
once the fan is moving air, then a number of safety switches keep an eye on temperature of heat exchanger, flue, blower compartment, and flame roll out etc etc...
So by reading that, watch your furnace light off. Go thru the s.o.o. and that will help you to describe your problem and possibly help YOU to diagnose it. Just by what you have described, it sounds as if the flame sensor is dirty and not sensing flame on the first or second try.
Pull it out and clean it with emery cloth or light sand paper. Also, i dont care when you changed the filter last, change it again.
Check back in and let us know. Hopefully this will help you to either fix it or describe the problem better. But from where i am sitting it sounds like you just need to have the unit serviced and maintained regularly. A good service guy will perform a pre season check up for 50-75 dollars and during that service
he will clean the flame sensor
check all the safetys
check the manifold pressure inlet and outlet
clean burners
check for carbon monoxide on older systems
check temperature differentials
check amp draw on motors
clean pressure switch port
and all of those things can mean the difference between a good running efficient home furnace and future problems and pre mature failure.