The English Language adverbs Specially and Especially are often confused, even by native English speakers. I will explain the difference using British English usage and examples.
Especially means "particularly", "exceptionally" or "above all others". For example "I love flowers, especially pink ones" means that I love pink flowers over and above flowers of other colours. "At the reunion, he was especially glad to see Sally again" means that he was glad to see many people, but in particular Sally.
Note that especially is an adverb and must be used to modify the meaning of a verb. You can't, therefore, write "especially today is happy" - this is wrong, the word especially in this sentence is not modifying the meaning of a verb, adjective or another adverb, as all adverbs must. Instead you should write something like "Today is especially happy" - especially is modifying the meaning of the adjective happy.
Specially means "for a specific purpose" or "specifically". The word is often used to describe something that has been created or designed for a specific purpose, for example, "the table was made specially for this room". It is also used to describe an action performed for a specific reason, for example "he played Bach on the piano, specially for Anne, as he knew she loved it so much".
In general if you can substitute the word specially for specifically it is normally the right word to use, just as if you can substitute the word especially for particularly it is normally being used correctly.
I hope this helps, but email me with any questions firstname.lastname@example.org