to go to the dogs = to become less successful, to deteriorate

My uncle likes to repeat that the country is going to the dogs.

To Go To The Dogs

 

every dog has its day = everyone is successful or happy at some time in their life

As they say, every dog has its day, so, be patient!

Every Dog Has Its Day

 

the hair of the dog (that bit you) = an alcoholic drink that people drink to alleviate hangover.

It seems I had one too many last night. Need some hair of the dog.

The Hair Of The Dog

 

to lead a dog’s life = to lead a miserable existence

I’m tired of leading a dog’s life.

To Lead A Dogs Life 1

 

dog-tired = extremely tired

Every day I come home dog-tired and fall asleep at once.

Dog Tired