As i recently did this trip, i thought i will provide my 2 cents on this travel , so that others can use this
there are three ways of reaching from Iasi to Chisinau
1) Train - Take a taxi from Iasi airport to Socola train station (should cost you 25-30 RON) and then there is train on saturdays and sunday evening (5:20 PM) which takes around 3 hours and less hassle as there is no wait on passport control. However there is no facility to provide on arrival visa on this route, so make sure that you have the required visa for Moldova
2) Bus - Take the bus from outside the airport to the Autogara (should be 2 RON) and then you get the Minibus from Autogara having every hour. should cost you 30 RON. However the last bus is at 5:30 PM and generally the last two buses get reserved. so make sure that you arrive atleast an hour before the bus departs to confirm a seat on the minibus.
3) Taxi - When all the mini buses have left, there will be taxis available. Ask for a taxi to Chisinau and some one will guide you to the supermarket (name starts with M, which i forgot) from where you will get a taxi share. They will charge you 50 RON for the 3 hour trip and they generally dont face much traffic at the passport control
As i was quite late at arriving at the autogara i took the 3rd option