Conditional Perfect Progressive

Use
We use it for something that might have happened in the past.
We use it in the main clause in type III of the if clauses.

Form
would + have + been + infinitive + ing

Example
Maria would have been singing if there had been more people in the church.

Conditional Perfect

Use
We use it for something that might have happened in the past.
We use it in the main clause in type III of the if clauses.

Form
would + have + past participle
past participle -> (infinitive + -ed) or (3rd column of the table of the irregular verbs)

Example
I would have phoned you if you hadn't switched your mobile off.

Conditional Progressive

Use
We use it for something that might happen.
We use it in the main clause in type II of the Conditional sentences.

Form
would + infinitive

Example
I would fly to Sydney if I had the money.

Conditional Simple

Use
We use it for something that might happen.
We use it in the main clause in type II of the Conditional sentences.

Form
would + infinitive

Example
I would fly to Sydney if I had the money.