I asked her to wait a moment.

Literal

I [topic-は], her [to-に] a-moment wait-give [so-as-to-ように] asked.

The pattern [verb]+ように+頼む is the standard way to report an indirect request — 'ask [someone] to [verb].' The verb inside is くれる ('give, do for me'), which is mandatory when the request is for the speaker's benefit. Combined: ちょっと待ってくれるように頼んだ = 'asked her to wait for me a moment.'