grammar - What's the best way to find the subject in a sentence?

What's the best way to find the subject in a sentence?

How do you define a subject?
I am especially curious about such cases, in which the subject seems to be represented by more than one word:

The majority of people didn't mind the new policy.

A great number of students went on strike yesterday.

Addition:

and such cases where the passive voice is used:

The man was bit by a dog.

Children were frightened by the wolf.

Also, please, consider such cases with ergative verbs:

I broke my chair.

The chair broke.

The chair was broken by me.

Answer

Subjects are noun phrases, and usually have more than one word in them, but they can be just one word, if there are no modifiers. Subject is a grammatical concept restricted to languages with nominative-accusative systems,
like most Indo-European languages. Languages like Basque, Georgian, Quiché, or Pitjantjatjara,
which have absolutive-ergative systems, do not support a meaningful concept of Subject.

Virtually all tensed English clauses (including all simple sentences), require a Subject constituent.
Besides its position before the verb phrase, the grammatical properties of a Subject include:

• number agreement with the verb phrase
  The ladies are arriving ~ The lady is arriving


• inversion with auxiliary in questions
  The old man in the trenchcoat is coming => Is the old man in the trenchcoat coming?


• pronominalization in tag questions
  Those guys are the ones, aren't they?


• upstairs control of A-Equi deletion, plus downstairs deletion by Equi
  Bill wanted to see the painting = Bill wanted (for Bill) to see the painting.


• promotion by Subject-Raising (often obligatory)
  *For there to be beer in the fridge tends => There tends to be beer in the fridge.


• movement and optional deletion by Passive
  Acme Construction erected this building in 1936 => This building was erected in 1936.


• contraction with auxiliary (especially pronouns)
  The old woman has/is gone now => The old woman's gone now

In addition, there are semantic criteria governed by predicates. Most predicates will only accept certain types of noun phrase as subjects, and lots of tests can be fashioned with different verbs.