Where you could replace should with ought to and it would have more or less the same meaning, then a common translation in French is to use the conditional tense of the verb devoir. As in English, it is followed by the infinitive. For example:
The formula should have ... is translated into French using the conditional perfect of devoir. This means that you use:
Note from the last example that you can say shouldn't have by negating the verb in the usual way.
In formal, old-fashioned usage, should is sometimes used to mean would.
Since using should in this way is essentially formal (and for many speakers old-fashioned), you could try to find a formal verb in French. For example, for I should like ... a possibility is to say j'aimerais ... or je souhaiterais ... rather than je voudrais .... It's often not possible to make such a distinction in French, however.
In English, the construction if I/you should ... is sometimes used to mean something similar to if ever I/you .... In French, a possible translation is therefore to use si jamais ... ("if ever ..."):
In formal or careful usage, English sometimes uses should to emphasise the speaker's reaction to something rather than stating that something has taken place. (In a formal analysis, this is sometimes called a non-assertion.) For example:
In this sentence, the speaker chooses to say should decide rather than decided to emphasise their reaction to the decision rather than simply stating that the decision was made.
In French, this use of should generally corresponds to the subjunctive. The subjunctive is a special verb form used to make a non-assertion. (English no longer has subjunctive forms of the verb; the nearest equivalent to the subjunctive in English is using other constructions such as should ..., might ... as in the above example.) So to translate the above example into French using the subjunctive, we might say:
The construction ait décidé means roughly the same as a décidé = (has) decided, but ait is the subjunctive form of avoir rather than the usual present tense form that you'd use to form the perfect tense.
How to translate would into French
What is the subjunctive?