The present conditional tense corresponds to "would."  It is used after the imperfect in a conditional sentence.  Most conditionals sentences begin with si (if).  Si j'étais (imperfect) dans une autre famille, est-ce que je serais (conditional) plus heureuse?  If I were in another family, would I be happier?  However, do not confuse the conditional would with the would that expresses a repeated action in the past.  If would means used to, then the imperfect tense is used.  Quand nous étions (imperfect) en vacances, nous dormions (imperfect) jusqu'à midi.  When we were on vacation, we would (used to) sleep until noon.

To form, use the infinitive and add the imperfect endings.  But remember to drop the -e on -re verbs.

Also, you use the same irregular stems and exceptions for the conditional that are used for the future tense.  You may have noticed that the future and conditional forms for je seem to be pronounced the same.  Actually, the future ending is pronounced ay and the conditional like eh.  However, it is difficult to understand the differences in spoken French and most people pronounce them the same anyway.

The past conditional is formed by using the conditional of avoir or être and a past participle.  It corresponds to "would have" and is used in hypothetical sentences.

Il n'aurait jamais dit ça!  He would have never said that!

If... sentences

When si (if) is used in sentences of condition, the verb tenses change.  These pretty much correspond to English usage.

1.  Si + present tense + present, imperative, or future
Si je suis fatiguée, je me repose.  If I'm tired, I rest.
Repose-toi si tu es fatigué.  Rest if you're tired.
Si je suis fatigué demain, je me reposerai.  If I am tired tomorrow, I will rest.

2.  Si + imperfect + present conditional
Si j'étais riche, je pourrais acheter un château.  If I were rich, I would buy a castle.
Il deviendrait roi s'il avait plus de courage.  He would become king if he had more courage.

3.  Si + pluperfect + past conditional
Si j'avais su, j'aurais compris.  If I had known, I would have understood.

It is possible to have past conditional with the imperfect, and it is also possible to have present conditional with pluperfect.  However, you can never have the future or conditional tenses directly following si.  They must be in the other clause.  (This is a rule in English too... you can't say "If I will go tomorrow")

To Drive

The past participle of conduire is conduit.  Other verbs conjugated like conduire are: traduire - to translate, produire - to produce, and construire - to construct.