Modal verb: Ought to

"..People ought to know several things about the recent history.."





Ought is different from other auxiliary verbs. It is used with to.
We can use ought to instead of should in some contests.
example:
- Do you think I ought to apply for this course in particular?
- Yesterday it was a useful lesson in the university. You ought to have come.
- He has been studying hard for the exam, so he ought to pass.

Ought expresses duty, necessity, desirability and similar ideas. It is often used to advise people: to tell them that they have a duty to do things. The meaning is similar to should, is not as forceful as must. 
examples:
- You ought to attend school regularly. (Duty)
- You ought to help the needy. (Moral obligation)
- We ought to buy a new car, the other one has broken down. (Necessity)


NOTE:
Note that to is dropped in question tags.
- You ought to love your girlfriend, ought not you? (NOT…ought not you to.) 

Ought does not have infinitives (to ought) or participles (oughting, oughted). Questions and negatives are made without do.


BUT:
Ought is rarely used in questions and negatives; should is generally used instead. A structure with think … ought is also common.
examples:
- We ought to help them, shouldn’t we? (More natural than ought not we?)
- Do you think I ought to consult a doctor? (More natural than Ought I to consult a doctor?) 
- Should we tell her? (Less formal than Ought we to tell her?)

Modal verb: Should

example:

Here the scientist suggests to his colleague:
"I think you should be more explicit here in step two..instead of writing then we need a miracle..."







You should do something = means it is the right thing (or a good thing) to do
Should is used to give advice or to give an opinion.
examples:
- Your English needs a review. You should study some grammar.
- The government should do something concrete to help this country.
- Should we invite Mark for my birthday? Of course, we should! 
- You shouldn't run, is very slippery.  (negative form)

• Should is not as strong as must or have to: - You should apologise to her (it would be a good thing to do) ; You must / have to apologise to her (you have no alternative)

• It is possible to use should when something is not right or what we expect: - I wonder where Matteo is. He should be already here by now; - The price of this book is wrong, it should be 10€ not 100€

• Should can be used to comment on something we expect: - There shouldn't be any problem on finding a Hostel in Barcelona in two weeks.

• Should is often used after some verbs like: DEMAND, INSIST, PROPOSE, RECOMMEND, SUGGEST

ALSO
Should is often used in the first conditional hypothetical constructions:                     if + should + infinitive:

example
- If you should happen to miss the train, I could drive you there myself.

- Should you wish to change your holiday arrangements, we will all we can to help.  (very formal situation, in written English)

we are going to review conditional situations a bit further