The simple predicate is the verb or the essential parts of the verb phrase —the parts which cannot be omitted without changing the meaning—in a sentence. In a sentence with a simple verb, the simple predicate is easy to identify:
She looked up at the sky.
In a sentence which contains an auxiliary or linking verb, the simple predicate also includes them:
She was looking up at the sky.
She has been looking up at the sky.
In a sentence which contains a phrasal verb, the essential parts of the phrasal verb are also part of the simple predicate:
She looked up his phone number in the directory.
She was looking forward to calling him.
Even when the parts of a phrasal verb are separated by other words, they are part of the simple predicate:
She was looking his phone number up in the directory.