My father can speak English well.

Literal

Father [topic-は] English [object-を] skillfully speak thing [subject-が] can-do.

~ことができる is the formal way to express ability — more explicit than the potential verb form 話せる. 上手に is the adverbial form of the na-adjective 上手 ('skilled'). 出来る here is written in kanji rather than hiragana できる, giving it a slightly more formal feel.