The conditional tense (sometimes described as the conditional mood) is a verb form in many languages, in which a verb root is modified to form verb tenses, moods, or aspects expressing degrees of certainty or uncertainty and hypothesis about past, present, or future. However, the English language is structured radically differently from many languages in that verbs do not conjugate in the same way, and it therefore becomes impossible to identify a conjugated verb form that may be identified as conditional.

But of course English speakers still need to say things conditionally, and so the existence of a non-conjugated form in the English language which is parallel to the conditional verb form of other languages can be identified.

English has four forms of conditional, conventionally called the zero, first, second, and third. Here are examples of each:

Zero conditional

If water is heated to 100 degrees, it boils.
Whenever it rains, I take my umbrella.
You can see that the conditional has two distinct verb groups: the condition (if water is heated) and the result (it boils). Both groups use a simple present tense in English in the zero condition, and they express some kind of universality.

First conditional

If it rains, I'll get wet.
If you ring me, I'll come.
Here, the condition verb group is still present: we are still expressing universality. However, there is a degree of choice implied in the consequence, and so the modal will is used. In more marked forms, it is possible to substitute WILL with other first dimension modals (can, may, shall, dare). If you ring me I (may/shall/can/dare) come.

Second conditional

If I were you, I would talk to her.
If you rang me, I would come.
Both verb groups have performed a standard exercise in English tense behaviour: they have backstepped. The simple present of zero and first conditionals has moved to a simple past (if you rang me - though this may in fact be subjunctive past) and the first dimension modal will has become the second dimension would. That is, in order to make the meaning more remote, the verbs have moved away from the present. This degree of remoteness may be required by courtesy.
If you passed me the salt, I'd be happy
The formal structure of the second conditional is:
If + simple past, would + verb
Again, would can be substituted in marked forms by other second dimension modals (could, should, might).
If you rang me, I (would/could/might/should) be able to come.

Third conditional

If you had rung me, I would have come.
A further stage back: hypothesis as to how the past could have been different, but wasn't.
If + past perfect, would (have done)
In the conditional phrase "If I were king, you would be queen", were is subjunctive while would be expresses a conditional. Similarly, "Could you bring me a glass of water?" is a polite form of "Bring me a glass of water!"