Sentence Fragments

A sentence fragment lacks the ingredients of a sentence, such as a subject, a complete verb, or making complete sense. 
Examples of fragments are as follows:
Talking on the phone.
Paper plates and cups strewn all over the lawn.
Although I am contented with my job.
Subject
In order to correct fragments, the first thing to do is ask the question: Does the statement have a subject?  If one is missing, adding a subject can turn the fragment into a sentence.
Picked up milk from the grocery.  (Who did?)
By adding the subject Saman, the statement will be a complete one:
         Saman picked up milk from the grocery.
Complete Predicate
Another question, you should ask: Does the statement have a complete verb?
She talking on the phone.
The verb is incomplete. 
By adding the helping verb is, the statement becomes complete.
She is talking on the phone.
Another thing that can create a fragment is the use of ing or to verb at the beginning or end of a sentence.
Kumar was sick.  Fighting a virus for a week.
The second statement is a fragment, which can be corrected by replacing the period with a comma after sick and making a of appearing into a lower case.
Kumar was sick, fighting a virus for a week