Istanbul Atatürk Airport

Named after Mustafa Kemal Atatürk, the founder of modern Turkey, Istanbul Atatürk Airport is located 20 km west of the city centre of Istanbul, the country's largest city. As Istanbul is situated partly in Europe and partly in Asia, it's one of only two major airports in the world that can be said to serve two continents (the other being Sabiha Gökçen, on the Asian side).
A military airfield was established in the location what was then the countryside in the outskirts of the city in 1911, before the collapse of the Ottoman Empire. The first civilian flight out of the airport was conducted in 1933 to Ankara, the capital of the Turkish Republic. The international flights began in 1953. Since the 1970s, the airport is increasingly engulfed by urban development on all sides, which prevents further expansion. As a result, the construction of a third airport for the city, near the Black Sea coast in the north, has started in 2013.

Visa

You probably need a visa to enter Turkey, which can usually be obtained online. Check if this applies to you, and apply in advance. Do not rely upon any other website, including Wikivoyage, as the rules may change suddenly as the security situation in Turkey evolves. Also some websites charge extra for no additional service. In general EU Schengen passport holders need no visa to enter, North American and UK residents need a visa costing US$20 valid for 90 days, residents of China pay US$60 for 30 days, and visa duration and price varies for other nations. Some travellers are not eligible for an evisa and must apply for a conventional visa via their local Turkish Embassy.
Apply at the same time as you book your trip - your 90 (or other) day visa validity will start from your stated arrival day in Turkey. Print it out and keep it with you, as well as a soft copy on your phone. It will be checked when flying, and could be demanded at an internal police check, such as those on highways between cities.
In theory you are permitted to arrive at Ataturk Airport without a visa and use the visa office or self-service machine to apply there.  There is no similar facility at Sabiha Gokcen or other Turkish airports or at the land or sea borders, but you could apply online by mobile phone anywhere, anytime. There is no sense whatever in leaving it so late. The check-in clerk would be quite entitled to turn you away to sort yourself out then re-join the back of the queue; and then suppose the evisa website was offline for any reason?

Just about every major city in Europe (including European Russia) has a direct flight to IST, and there are extensive connections across the Middle East, and links to the Far East, Africa and North America. Many of these are operated by the national carrier Turkish Airlines, either itself or by code-share. International flights use Terminal 1/the International Terminal: this includes flights to Ercan in Northern Cyprus, not recognised by other countries.
All major cities in Turkey, and quite a few medium-sized towns, have at least a daily flight to IST, and those from Ankara fly hourly. Domestic flights use the older Terminal 2 (aka the Domestic Terminal). The two terminals are a short walk apart via a corridor; the main delay is in clearing immigration inbound and outbound, so you need to factor this in when transferring.

People get commissions by persuading you to use special shuttle buses for very high fees (over 30 TL). For people who wish to travel more economically, the Metro/tram-combination is easy and fairly quick and offers very good value.

By taxi

Taxi from the airport to Taksim costs about 40–60 TL, also about the same to Sultanahmet in the old city. There are no night fares in Istanbul any more. The price would be the same at midnight or midday.

By bus

The express bus service run by the local airport service called "Havataş" which departs half-hourly 04:00-23:59 and costs 11 TL to Taksim, Aksaray, and Kozyatağı. The public bus (line #96T) run by İETT (the municipal bus organization) costs 5 TL (T
3.5 TL with an İstanbulKart), which has fewer departure times now due to Havataş.

By light rail

The metro operates 06:00-23:59 and is signposted "light rail" in the airport. When you get outside the baggage claim, it's about a ten-minute walk in the airport to the metro line (M1A). This line will take you directly to the Otogar (bus station) or to numerous stops within Istanbul (Yenikapı in the city centre is the last stop, the transfer stations for the tram heading for deeper into the old city is available at Zeytinburnu and Aksaray). It costs 4 TL, by token (and an extra 4 TL when boarding the tram) and getting to Aksaray takes around 45 minutes. It is possible to be at your bus departing from Otogar within less than one hour after landing by taking the metro. If you are going to Beyoğlu, you can change to the green line (M2) at Yenikapı and take the metro to Şişhane or Taksim.
When entering the metro station, you need to buy a jeton (token) for 4 TL. Just hand the cashier 4 TK and he'll give you a token, or use the automatic dispenser (Jetonmatik), which accepts banknotes (5 TL, 10 TL) and coins. Use 'select' to choose the number of jetons and then push 'ok'. They don't accept credit cards or foreign currency here. This will get you on the red metro line (towards Yenikapı). From this line, if you are going to Sultanahmet, you can transfer at Zeytinburnu you will need a second token for the transfer. From Zeytinburnu, take the blue tram line T1, towards Kabataş which passes by: Sultanahmet, Eminönü and Tophane. The trip from the airport to Sultanahmet takes about 60 min. Also consider buying an Istanbulkart (see Get around on Istanbul's page) which will pay for itself within a few trips on public transit.

Unlike many other airports, you must go through the security check twice: once before entering the terminal building itself, and another time before entering the area of the gates. Also expect to find huge queues at the immigration check both when entering and exiting the country, so take these into account when planning your timetable. (Showing up at the airport a minimum of two hours before your international flight, and an hour before a domestic one, is usually recommended.)

Turkish Airlines offers free guided tours of Istanbul's sights to their passengers under a program called Touristanbul. This program includes transport from and to the airport and a traditional Turkish meal. There are different tours each day of the week taking either six or nine hours. The conditions are: you need to have a layover of at least six hours and at most 24 hours, between 09:00 and 18:00 and, in addition, both your arriving and departing flights must be international and operated by Turkish Airlines. No prior reservation is needed for these tours, you only need to proceed through customs and immigration and after that to the "hotel desk" in the arrival hall. The airline has more detailed information on their home page. Remember to check if you need a visa to enter Turkey.

Lounges

• Emirates Lounge

Food and drink at the airport may cost up to five times more than in the city proper, as in other international airports. If you are travelling on a budget and plan to spend some time at the airport, it may be wise to bring your own meals from town instead of buying them there. If you come from the Metro, there is a supermarket in the tunnel leading to the elevators and stairs to the airport where you can do some last-minute shopping.

As at most airports, money exchange is more expensive than in the city, but the rates are not egregious. In Istanbul the airport money exchange offices accept few currencies. It is recommended to bring US dollars or euros for the best exchange rates. There are many ATMs available for withdrawing Turkish lira and other currencies.
The supermarket in the tunnel leading from the metro station mentioned above has prices close to the city centre average.
When entering the country, there is a large duty-free shop after the passport, and before the customs check.

There is a single on-site hotel in the airport.

• TAB Airport Hotel

  phone: +90 212 425 40 30
  address: Atatürk Airport International Terminal
  The hotel has landside and airside entrances. The airside entrance is in the "international zone" (after the immigration when leaving, or before the immigration when entering the country), and it is possible to rent rooms per hour.

There are many hotels in the surrounding suburbs.

The pleasant seaside suburb of Yeşilköy, just to the south of the airport (10 minutes by taxi; no direct public transportation), has beautiful historic houses, many restaurants and cafes, and a long seafront promenade where you can stretch your legs.