French Conditional Mood - Conditionnel
Conjugations

Source:  http://french.about.com/library/weekly/aa121299.htm

To form the conditional of -ER and -IR verbs, add the appropriate ending to the infinitive. For       -RE verbs, drop the final E before adding the ending.

The only irregular conditional conjugations occur in about two dozen verbs which have irregular stems but use the same conditional endings listed above. Here are the French verbs with irregular conditional stems:*

*Notes:

1. The exact same verbs are irregular in future conjugations.
2. The conditional stem always ends in R.

Here are examples of -ER, -IR, -RE, and irregular verbs in the conditional:

Uses of the conditional:

The conditional is a verb mood used for events that are not guaranteed to occur; often they are dependent on certain conditions. It is translated as would in English. 

The French conditional is mainly used in si clauses: if ___ then ___.  Pattern is “if imparfait, then conditional”—If I was in France, I would eat a crêpe.

Il mangerait s'il avait faim - He would eat if he were hungry.
Si nous étudiions, nous serions plus intelligents - If we studied, (then) we would be smarter.

The verb vouloir is used in the conditional to express a polite request:

Je voudrais une pomme - I would like an apple
Je voudrais aller avec vous - I would like to go with you.

However, you can't say "si vous voudriez" to mean "if you would like," because the conditional can never be used after si - learn more.

The verb aimer is used to express a polite desire, sometimes one that cannot be fulfilled:

J'aimerais bien le voir ! - I would really like to see it!
J'aimerais y aller, mais je dois travailler - I would like to go, but I have to work.