She is as busy as Tom.

Literal

She [topic-は] Tom [as-と] same-degree busy.

と同じくらい is the standard 'as ___ as' construction: と marks the comparison standard, 同じ means 'same,' and くらい is a degree marker — literally 'to the same degree as Tom.' Replacing くらい with ほど (~と同じほど) is also valid and feels slightly more written or formal.