Southern half of the region is fairly shadeless plains (sometimes totally flat as far as eye can see) dominated by steppes that are bright yellow in summer. Northern half is hillier, but still mostly devoid of trees nonetheless.
Two major rivers of Middle East, namely Euphrates (Turkish: Fırat) and Tigris (Turkish: Dicle), after originating from the snowy mountains of Eastern Anatolia, flow through the region with many of region's cities and sites either directly on or near either one's banks, and then cross Turkey's southern border into Syria and Iraq.
While you may occasionally come across a tout in more touristy parts (eg Urfa) or kids asking for money—which is pretty much the full extent of their English vocabulary, apart from the ubiquitous hello—normally, the local people are extremely hospitable and friendly (sometimes to a fault) and are willing to help you in any way they can—they are just proud that, after so many years of armed conflict and political instability, travellers from far away places are now making the effort to see their hometowns.
Looking from outside, Southeastern Anatolia may seem to be inhabited by Kurds only, but when looking closer, you will find a diverse array of religions and ethnicities in the region, although not up to the levels once found during the Ottoman period.
Western quarter of the region, west of Euphrates River to be more precisely, are mostly populated by Turks, with villages populated by Kurds here and there. The majority of population east of Euphrates, on the other hand, is Kurdish.
Ancient Tur Abdin region in the southeast, centred around Mardin and western half of Şırnak Province, and historically dominated by Orthodox Christian Syriacs ("Suryaniler"), is an altogether different story. Amongst the inhabitants of this region are Yazidis, a Kurdish-speaking people with a fairly unique belief system—which leads to them being derogatorily called "heathens" or "original Satanists" by other locals and non-locals alike. Yazidi belief system combines influences from Sufi Islam and ancient Mesopotamian and Persian religions, in which Melek Taus, symbolized by a peacock and usually compared to the "satan" figure of Abrahamic religions—a comparison that Yazidis find highly offensive—is a highly revered entity, and seen as the source of light and representative of God on Earth. The major rites of Yazidis, in which the participants face the Sun, are conducted on hilltops twice daily, during sunrise and sunset. Nowadays, Yazidis, most of whom emigrated from the region, keep a low profile and live in fairly off the beaten path villages, as a result of centuries of repression as well as religious commands to stay away from non-Yazidis.
There was also a sizable Armenian population in Southeastern Anatolia, but the events of 1915 hit the community hard. Nowadays, there is a handful of mostly elder Armenians in the region, mainly in Diyarbakır.
In addition to these sedentary peoples, there are also nomadic Kurds, who pass the winter in the relatively warmer region and move on to the cooler plateaus of Eastern Anatolia with their herds in summer, in search of pasture.
While it is hot in absolute terms with temperature frequently above 40°C, rainless summers in Southeastern Anatolia tend to be more comfortable, at least in shade, than Mediterranean Turkey which lies on the same latitude, thanks to the low humidity of this arid, non-coastal climate. Snowfall is occasional in winter and generally happens in relatively hillier eastern and northern parts of the region (i.e. around Mardin, Batman, and Diyarbakır).
In Southeastern Anatolia, the Euphrates River (Fırat) forms some sort of linguistic boundary: west of the Euphrates is mostly Turkish speaking with a Kurdish-speaking minority while the mother tongue of most of the locals living east of the Euphrates is Kurdish. However, most locals in the region are also bilingual in Turkish, although heavily accented in most cases.
While traveling in southeastern Anatolia, it is important to be conscious of whom you are speaking with. At military checkpoints, Turkish and English will suffice (most Turkish officers speak some English, usually due to previous training in the United States); it is critical not to test your smattering of Kurdish words with the Turkish military. When amongst Kurdish friends, the Kurdish language is appropriate, but be sure not to place your hosts in an uncomfortable situation by speaking in Kurdish while other Turks are present.
Arabic might also be useful as it is the mother tongue of many people living in the western and southern parts of the region, especially in and around Gaziantep, Sanliurfa, Hasankeyf, and Siirt. Syriac, also known as Assyrian, a direct descendent of Jesus Christ's mother tongue Aramaic, can also be heard spoken by small communities in and around Mardin and Midyat.
Many Arabic and Farsi expressions have made their way into the local vernacular.
While not on the same level as the buses in western Anatolia, bus service into and throughout southeastern Anatolia is decent enough with services from major centres throughout the country. You'll find buses running between most major destinations daily (oftentimes more than once daily). In the very deep southeast around Sirnak, Beytussebap and Hakkari, dolmuş (shared van-taxis) and minibuses are far more common but do not run as frequently or on as tight a schedule.
Diyarbakır and Batman have three times weekly train services (Güney Express) with Istanbul via the interior of the country, including a stop in Ankara, the national capital. Toros Express which offered some impressive mountainous scenery and connected Gaziantep with Istanbul via Konya and Adana, on the other hand, has been suspended in 2008 and it is not certain when or if it will resume service. However, Gaziantep has a recently introduced weekly passenger train service from the opposite direction, Mosul in northwestern Iraq, crossing a short strip of Syrian territory and running on the rail line just north of no man's land along Turkish-Syrian border. (Update, August 2010. Mosul service has been suspended until further notice.) Gaziantep also has twice weekly direct train connections with the major Syrian city of Aleppo.
Bus and minibus service is generally robust, although schedules are not closely adhered to and you may find yourself waiting an extra hour or two for that minibus that everyone has been promising will arrive soon. Private vehicles often serve as taxis but for fees that are higher than one would expect. Be ready to haggle. Hitchhiking is far easier than anywhere else in Turkey, with lift offers generally coming from the first vehicle passing by. It's pretty much safe, too, as long as you stick on the main roads at least. In the past, however, it's known that PKK have raided private traffic on roads in deeper southeastern Anatolia.
Many roads in the region is full of potholes and locals drive somewhat recklessly, even more so than the rest of the country, so be extra careful if you are the one who is driving actually.
Local cuisine is heavily dependent on meaty fare, with Gaziantep and Urfa being renowned nationwide for their local varieties of kebabs. Vegetarians will have a tough time in the region and should prepare themselves for ransacking supermarkets for canned vegetable meals and eating lots of unsavory and unexciting pastry.
A local product not to be missed is pistachio, grown in the countryside surrounding Gaziantep and Siirt, in the southwest and northeast of the region respectively. While it is known as Antep fıstığı (i.e. "pistachio of Gaziantep") in Turkish, people of Siirt vehemently object to this name, and prefering to call it instead as Siirt fıstığı ("pistachio of Siirt") or with the local name bıttım, mostly unknown in the rest of the country. Gaziantep variety is smaller and tastier, but both are worth a try.
Tea ("chay"): it's everywhere. Be sure to add copious amounts of sugar to blend in with the local population. Anything less than three cubes just won't do.
Stay abreast of the news in northern Iraq and southeastern Turkey before and during your visit to the region. The politics of the region is very fluid with the Turkish government threatening military intervention into northern Iraq and the Kurdistan Workers' Party (PKK) making raids on military outposts. The Turkish military will sometimes declare curfews on entire cities in the area, making civilian travel to the region impossible. It is often best to talk to fellow travelers in Istanbul, Ankara or, even better, Diyarbakir before making your way into the deep southeast. Don't trust the Istanbulites who will suggest that you won't live through any visit east of Ankara. A vast majority of them have never left Istanbul. A trip to southeastern Anatolia is very much feasible and, for the most part, safe. The deep southeast should be done with more caution, but it too is possible for the hardy traveler.
On some non-major routes, you may run into a few military checkpoints, though all you need to do is showing your passport (therefore keep it handy during rides, not buried deep in your backpack). Keeping a short list of cities on your itinerary in mind may save time in case of further questioning at checkpoints.
The arid climate in Southeastern Anatolia can quickly dry your skin, especially your hands, and especially if you have a sensitive skin and/or are normally living in a humid, coastal climate. So don't forget to pack along some kind of moisturizer if you intend to stay more than a few days in the region.
Being not accustomed to heavily spicy/hot food, in addition to the fact that some food are prepared in less than perfectly hygienic ways, may lead to stomach trouble in some travellers whilst in the region.
Don't; it's far too beautiful.
Heading west from Southeastern Anatolia, if you have not already arrived from that direction, will make you meet the warm waters of Mediterranean Turkey, a totally different world. But if you rather prefer to chill than to sunbathe, then head north and east into the mountainous realm of Eastern Anatolia.
Warning: the Middle East is just south of the border, which can be crossed via a number of border gates south of Gaziantep, Urfa, and Mardin. Please note that the area is under massive unrest facing high levels of terrorism and violence.