Find a drone source comfortably in your vocal range.  Something that creates a droning in-tune sustained note.  You can pluck your guitar repeatedly or put your forehead on your refrigerator.  Or use a recording of  a drone.  The best is an Indian Tamboura.  There are recordings available online.

Now hum this note a few times.  

Now sing the word “Sa” to this note ten or twenty times.  Let your tongue fall into the bottom of your mouth, like you are saying “Ah” for the doctor.  Open your throat.  Long gentle comfortable “Sa.”  Try to settle your pitch perfectly inside the pitch of the drone. 

Do this every day for a few months.  Find a time when you can do it every day.  Perhaps every morning in the shower or on your way to work.  

Also.  Try to slightly varying your pitch out of tune either sharp or flat.  Vary it by less than one half step.  Try to vary it by a quarter of a half step.  And then return to the true pitch.  Experiment with how small of a variation you can hear in your voice?

Sing Sa will do more for your ability to sing freely and to hear pitch clearly than any other activity.