This tense is quite simple to make. Simply take an word, such as 'fine' or 'tired', and add the word 'değil'. This is not a suffix, but a word on its own. Then add the same personal endings that you would for the 'to be - positive tense'.
examples
'iyi değilim' = 'i am not fine'
'mutlu değilsin' = 'you are not happy'
'yorgun değil' = 'he is not tired'
'Türk değiliz' = 'we are not Turkish'
'yorgun değilsiniz' = 'you are not tired'
'iyi değiller' = 'they are not fine'
Past Tense
To turn this into the past tense, such as 'he was not happy', add the past suffix '-di' and then the personal ending, just like with the 'To be - positive' tense.
examples
'iyi değildim' = 'i was not fine'
'mutlu değildin' = 'you were not happy'
etc
Asking Questions
To turn this tense into a question, follow this formula;
word + değil + question + personal
mutlu + değil + mi + sin
= 'mutlu değil misin?' = 'are not happy?'
'mutlu değil miydin?' = 'were you not happy?'
'yorgun değil miyim?' = 'am i not tired?'
'yorgun değil miydin?'= 'were you not tired?'
'iyi değiller mi?' = 'are they not alright?'
(For 'they', the question marker comes at the end).