'I look forward for' is not correct. It should be 'I look forward to'. e.g. I look forward to meeting you / I look forward to our meeting. It is the same for I am looking forward to. e.g. I am looking forward to the weekend / I am looking forward to seeing family at the weekend. In all cases, '... forward to' is followed by a noun. A verb ending in 'ing' is a gerund - the noun form of a verb.

Both are correct but they give different emphasis. Both express hope but "to" gives a more positive outlook and a feeling of anticipation. "For" conveys more doubt. If you use "for", it will be attached to "look" as in "look for" so that it represents a search as well as a hope for something. If you use "to", it will be attached to "forward" as in "forward to" so that it represents anticipation. Here are some examples to clarify this: "I look forward TO the arrival of spring." (I can't wait! Spring will arrive after some time passes.) "I look forward TO eating lunch" (I am so hungry! Thank goodness I will eat lunch after time passes. Note: "eating" is a noun, not a verb. "Lunch" is the object of the participle in a noun clause.) "I look forward FOR better days to come." I am really looking. Perhaps better days will not come. This is an expression of hope mixed with doubt. I am looking FOR those days, but I have to look "forward" because I may not find them. If I said "to", it would have a different meaning. It would mean that I have a positive anticipation of better days to come.

Good Morning Oksana. Use ‘for’ with a noun and ‘to’ with a verb. I’m looking forward for my lunch. I’m looking forward to eating my lunch.

I agree with Claire. In the US I have only ever heard ‘looking forward to’ followed by a noun - an actual noun or gerund. Technically you could use ‘forward’ literally with ‘looking for’ but it’s not natural. Look ahead for a restaurant on the right. The turn off is 200m before it and unmarked. ‘Forward’ could replace ‘ahead’ here but it sounds awkward to me.