She runs faster than I do.

Literal

She [topic-は] me [than-より] fast runs.

The most basic comparative pattern: XはYより~ ('X is more ~ than Y'). 速く is the adverbial form of 速い ('fast') — modifying 走る ('run'). Note that Japanese has two homophone adjectives 速い ('fast in motion') and 早い ('early in time') — easy to confuse, and not always distinguished consistently in casual writing. For running, 速い is the correct kanji.