秘書はウイリアム氏が電話にでられるまで、そのまま待ってくれと私に頼んだ。

、。

The secretary asked me to hold while Mr. Williams was available to take the call.

Literal

Secretary [topic-は] Williams-Mr [subject-が] phone [to-に] can-come-out [until-まで], as-is wait [request-てくれと] me [to-に] asked.

電話にでられる uses the potential form: 'can come to the phone.' そのまま means 'as is, without change.' ~てくれと頼んだ combines a casual request (~てくれ) with quotative と and 頼む ('to ask').