Hopefully has two standard uses in modern English. First, it can be a sentence adverb, which means it comments on the whole sentence. In that use, hopefully means something like I hope or it is hoped.
Example: Hopefully, the train will be on time. Here, the word does not describe how the train will be on time. It expresses the speaker’s hope about the whole situation.
Second, hopefully can be an ordinary adverb of manner. In that use, it describes how someone does something.
Example: She smiled hopefully. This means her smile showed hope.
Some people were once taught to avoid the sentence adverb use, but it is now widely accepted in standard English. Context usually makes the meaning clear.
- Sentence adverb: Hopefully, we will finish early.
- Adverb of manner: The child looked hopefully at the door.
If you can replace hopefully with I hope, you are probably using the sentence adverb form.