Your place of arrival in Romania will be, most likely, Otopeni Airport near Bucharest. You can take a taxi/bus from the airport to the North Railway Station (Gara de Nord) in Bucharest, from where all the trains to Iasi leave.
There are several trains every day from Bucharest to Iasi. The best choice, due to the comfort provided, would be the InterCity (IC) train. The trip takes about 6 hours by the InterCity (IC) and about 7 hours by the Rapid (R) or Accelerate (Acc) trains. For information about the train schedule and ticket prices you can visit https://www.infofer.ro.

TIPS:

• It is advisable to take a taxi that is registered by any taxi company and not a private one (even if it bears the label “taxi”) from the airport to the railway station.
• It is always advisable to buy a 1st class train ticket. Train schedule can suffer small changes every year, so it is better to buy a ticket directly from the railway station and not to make a reservation before arrival.

If you decide to take the plane, you should know there are at least three airline companies that have flights to Iasi: Tarom Air Transport, Carpatair, and Austrian Airlines. Tarom Air Transport has two internal flights per day. The trip from Bucharest to Iasi takes about one hour. Carpatair has one internal flight per day, from Monday to Saturday. International Carpatair flights only come from Italy (cities: Torino, Bologna, Florence, Milano, Rome, Venice, Verona, Ancona) and from Germany (cities: Dusseldorf, Munchen, Stuttgart). You will have one stop and plane change in Timisoara. Austrian Airlines has one flight per day from Vienna to Iasi directly. Here are some flights to/from Iasi: Flights.

TIPS: When you reach Bucharest (Otopeni Airport) and you must change planes for Iasi, you must pick up your luggage and do the check-in again. Also, it is advisable to buy your plane ticket from a tourist agency, where you can be advised about the lowest prices and the most convenient flights.

A third possibility to reach Iasi is the minibus (maxi-taxi). There are several minibus stations near the North Railway Station (Gara de Nord) in Bucharest. There are at least 4 trips to Iasi organised per day. The trip takes about 6 hours.

TIPS: If you have a lot of luggage, the trip by minibus is less recommended, especially if there are many passengers.