A phrasal verb is a verb plus a preposition or adverb which creates a meaning different from the original verb.
Example:I ran into my teacher at the movies last night. run + into = meetHe ran away when he was 15. run + away = leave home
Phrasal verbs can be transitive and intrasitive.
An intransitive verb cannot be followed by an object. Example:He suddenly showed up. "show up" cannot take an object
A transitive verb can be followed by an object. Example:I made upthe story. "story" is the object of "make up"
Some transitive phrasal verbs are separable. The object is placed between the verb and the preposition. Example:I talkedmy motherinto letting me borrow the car.She lookedthe phone numberup.
Some transitive phrasal verbs are inseparable. The object is placed after the preposition. Example:I ran intoan old friend yesterday.They are looking intothe problem.
Some transitive phrasal verbs can take an object in both places. Example:I lookedthe numberup in the phone book.I looked upthe number in the phone book.
You should remember that native speakers of English tend to use phrasal verbs in everyday conversation and generally reserve one-word verbs (i.e. "investigate" instead of "look into") for more formal occasions such as business letters etc.
If you think of each phrasal verb as a separate verb with a specific meaning, you will be able to remember it more easily.