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She had a really great time at the party yesterday.
Literal
She [topic-は] yesterday party [at-で] very pleasantly spent-time.
楽しく過ごす ('spend time enjoyably') uses the adverbial form of 楽しい ('enjoyable, fun') with the verb 過ごす ('spend [time]'). Adverbial forms of i-adjectives end in ~く: 早く (quickly), 楽しく (enjoyably), 美味しく (deliciously). 過ごす is specifically for spending time — distinct from 使う ('use'), which is for spending money or other consumables. The で marks the location of the action: パーティーで is 'at the party.'