Special is a common adjective. Specially is its adverb form. Special means "particular, distinguished in a distinct way, or designed for a particular purpose." Specially means "particularly, in a distinguishing manner, or for a particular purpose." Especial is an uncommon adjective. Especially, its adverb form, is much more common. Especial means "exceptional, noteworthy, or particular." Especially means "exceptionally, in a noteworthy manner, or particularly." In the sense of "particular" or "particularly," the words mean pretty much the same thing. Often they can be used synonymously. However, if you want to stress the exceptional or noteworthy quality, then especial or especially is a better choice. If you want to stress the distinctive purpose of something, then special or specially is the word you are looking for.

Well said James. 99% of the time one can use "especially". The dress was made especially for her. The ice cream is especially good today.

Deep blue's answer is correct and very good, but a bit complicated. My answer is to use the word "especially" all of the time. I use "especially" for both of those words. The words are very similar and almost interchangeable. Also, don't worry about it because when you say it fast they sound the same. Many native English speakers mix them up all of the time. People will understand what you are saying even if you use the wrong one. Just say it 'specially fast...hahaha!