In the dictionary it says that 'gustaria' by itself is 'I would like'. I assume that you can put Yo in front of that for emphasis (as was mentioned in a previous lesson), but why in this case is there 'me'? Why don't you just say Gustaria or Yo gustaria?

the dictionary I use says "me" means "I" and "gustaria" means "like" but "me gustaria" means "I would like". Go figure. Then again, to a Spanish speaking person, "go figure" probably means "go do a math problem".

Hola. "Gustar" is one of a number of Spanish verbs that work very differently from English verbs. "Gustaría" does NOT mean "I would like." "Gustar" means "to give pleasure to" or "to please," so yes, you have to have a pronoun to indicate who is being given pleasure. "Me gustaría" means "it would give me pleasure" or, more colloquially, "I would like." Similarly, "me gusta" means "it gives me pleasure" -- that is, "I like." I strongly suggest that you find some good grammar resources. There are other messages in this forum that offer some online as well as in book form. You can't depend only on a dictionary.