I just don't get the reasoning behind which one is correct in which situation.
Typically I use the wrong one, or I use them when I'm not supposed to.
If you mean both in the sense of anticipating something, both are equally valid. However 'I look forward' is more formal; it's the kind of thing you would write in an official letter.
A typical example is the closing statement of a cover letter for a job application:
'I am looking forward' is less formal. You would rarely say to a friend on the phone 'I look forward to visiting you next week.' You would say:
I'm not sure why others here have suggested this is wrong. You wouldn't say 'I run towards the train station!', you'd say 'I am running towards the train station!'
Look forward to is a phrasal verb that means to await eagerly. It can be used in any tense. Examples:
cannot be interpreted to mean eagerly awaiting, as it would have to be followed by to_.
Thus, it can only mean one thing:
where forward is an adverb. This usage, however, is not common in regular conversation, except in very few circumstances. Nevertheless, it is definitely acceptable to say:
to indicate that one is eagerly awaiting an event.
Hmm, okay, a totally non-grammatical (probably, and thus very likely totally wrong) answer by an avowed non-grammarian (who nevertheless described and describes himself as a grammar-nazi at times):
"I'm looking forward to" means I'm doing it right now, this very instance, like in Elendil's example of being on the phone with a friend; I disagree that it's about formal vs non-formal, it's due to being on the phone with that friend in that moment, so of course you'd be looking forward to meeting said friend at that very moment.
"I look forward" means looking forward in a general sense; like, you'd not think about meeting your friend every second of the day, but the anticipation would be in the back of your mind all the time.
That's my take, and I'm sticking to it. ;-)
I look forward to seeing you means I await eagerly to see you.
I am looking forward means I am looking at the area in front of me.
Assuming you mean "I look forward to ..." and "I'm looking forward to ...", they are essentially the same thing. However, there is a slight difference. the -ing on "looking" is a present participle.
So if we consider "look forward to" to mean "anxiously await", then we can rewrite the phrase as:
"I anxiously await your visit", vs "I am Anxiously awaiting your visit".
So in this case, "look" and "await" are the verb, and "forward" and "anxiously" are the adverbs.
So it's sort of a active/passive thing. "I am" versus "I". You would not say "I looking forward to" or "I am look forward to". It is effectively the same thing as "I look" vs "I am looking". for example "I look good" and "I am looking good".
Look forward to something or look forward to doing something means "to excited and pleased about something that is going to happen"
But "I Look forward" can meaning with trivial differences according to the context. For example it can mean I'm looking to the area in front of my eyes.