I plan to call Tom tomorrow and ask him to help.

Literal

Tomorrow phone [by-で] Tom [to-に] contact and help-for-me [so-that-ように] ask intend-is.

A structurally rich sentence: 手伝ってくれるように頼む means 'ask (him) to help me,' where ~てくれる marks the help as benefiting the speaker and ~ように establishes the purpose clause for 頼む. 連絡して chains two sequential actions via te-form. 電話で uses instrumental で — 'by phone.'