I'm a native speaker. You can drop the "a mí" and simply say "Me gusta". Simple enough.
I don't want to throw you lots of grammar lessons beyond the useful resources already shared but basically, there are so many verbs in Spanish that in English they have an active subject (the doer) + a verb (the action) ex. I like, I eat, I miss, etc. BUT in Spanish (as in any other language) you can't assume there are exact translations of the same verbs you use in English, so in Spanish when "you like something" you are actually have a passive verb (and doer), which is "A mí me gusta" or "me gusta" which loosely might literally translate as "that is liked by me" instead of "I like it".