There are 2 international airports in Kyrgyzstan: Manas International Airport in Bishkek and Osh International Airport in southern capital.
Manas International Airport is situated in 23 km from Bishkek city. It takes about 40-50 minutes driving if there is no traffic jam.
Osh International Airport is in 9 km from the city. Transfer takes about 15-20 minutes.
If you did not order airport transfer, you can find lots of taxis outside. There are official ones like Manas taxi and they have a fixed price or just private taxi drivers who offer services in the meeting hall.
Approximate price for taxi service is about 9-11 $ in Bishkek and about 7 $ in Osh. But note please that it also depends on distance you are going to drive during your tour.
If you booked a personal guide or driver, they will meet you inside the airport at the meeting zone, as soon as you get out the arrival and baggage claim hall.