İstanbul's Atatürk International Airport uses the red and green channel system, randomly spot-checking passengers' luggage. You're allowed to import the following without paying duty:
Alcohol 1L of alcohol exceeding 22% volume, 2L of alcoholic beverages max 22% volume
Tobacco 600 cigarettes
Food 1kg each of chocolate, candy, coffee and tea
Currency No limit
Perfume & Cosmetics 5 bottles max 120mL
Note that it's illegal to take antiquities out of the country. Check http://english.gtb.gov.tr/ for more information.
Not required for some (predominantly European) nationalities; most other nationalities can obtain a 90-day visa electronically at www.evisa.gov.tr.
At the time of research, nationals of the following countries (among others) could enter Turkey for up to three months with only a valid passport (no visa required): Denmark, Finland, France, Germany, Greece, Israel, Italy, Japan, New Zealand, Sweden and Switzerland. Russians could enter for up to 60 days.
Nationals of the following countries (among others) needed to obtain an electronic visa (www.evisa.gov.tr) before their visit: Australia, Canada, China, India, Ireland, Mexico, Netherlands, Norway, Portugal, Spain, Taiwan, UK and USA. These visas were valid for between 30 and 90 days and for either a single entry or multiple entry, depending on the nationality. Visa fees cost US$15 to US$80, depending on nationality.
Your passport must have at least six months' validity remaining, or you may not be admitted into Turkey. See the website of the Ministry of Foreign Affairs (www.mfa.gov.tr) for the latest information.