I can swim as well as you.

Literal

I [topic-は] you [with-と] same-degree skillfully can-swim.

同じくらい ('about the same degree as') sets an equal comparison. 上手に ('skillfully') is the adverbial form of 上手. 泳げる is the potential form of 泳ぐ ('to swim'). と marks the person compared with.