Şırnak is a town in Southeastern Turkey.
Hitchhiking out of Sirnak is likely to require some walking as the city is situated on a hill and all road pass around the hill. However atleast it's downhill all the way. Be cautius as locals are overly helpful and are very likely to take you to the busstation even though you clearly tell them (in turkish) what you want to do.
South towards Cizre
From the centre just follow the signs and walk down the hill on the serpentine road for about 2 kilometers until you get to a petrol station. From there you can easily flag down a ride to Cizre.
East towards Hakkari
This is, by far, the most militarized road in Turkey and there's a scarcity of vehicles. However the hitchhiker who perseveres and brings with him/her a fair amount of time and a whole lote of patience will be generously rewarded as this is (in hitchhiker Theo's modest opinion) the most scenic road in Turkey.
From the city centre you simply ask people for directions to Hakkari Yolu (there are almost no signs). Once you get to the Jandarma base you'll be able to see where the road from the city intersects with the 'ring road' which dont pass through Sirnak. There's a great hitchhiking spot about 50 meter after the intersection. Either walk the 2 kilometers there or try to hitch a ride.
You're likely to end up drinking tea with some soldiers as their bases are always located at intersections.
Update: it's currently a war there now so you're not likely allowed to enter the road.