Two lines to start the translation:

Geceler çok soguk, sessiz ve karanlik

The nights are very cold, silent and dark

Anne, anne, annecigim

Mum, mum, my dear mum (or use mother)

and my try at some more

Yanimda olmani ne çok isterdim

Why do I so much want (you) to be with me?

Seni çok istedim hasretim anne

I really wanted you, I longed for you, mum

thank you soooooooo much but can you translate the whole song and it atarted with

Mazide kalan hatira gibi
Sevkatli kollarini aç bana anne

thaaaaaaaaaaaaaaaaaaaanks in advance

Sorry, as a learner I am struggling to translate more than this. 

Mazide kalan hatira gibi

In the past, like left over (remaining) memories
Sevkatli = ???? with ... love??

kollarini aç bana anne

open your arms to me mother