There are various budget airlines that fly directly into Istanbul Ataturk airport from all around the world.

If you are traveling from Europe and not in a hurry, we suggest you to take the train.
For more information on the trains from/to Europe to/from Istanbul, please check:
http://www.tcdd.gov.tr/tcdding/avrupa_ing.htm

For car hire, we recommend - www.avis.com.tr

There are various cruises and ferries that travels to or by Istanbul as well, please check with your local travel agencies since it depends on where you are traveling from.