Learn Hardcore Japanese: kinou ha haha ni denwa wo simasita.

は marks 昨日 (“yesterday”) as the topic of the sentence.
By using は on a time expression, you’re essentially saying “As for yesterday, …,” setting the time frame.
It can also carry a mild contrastive nuance (“yesterday (as opposed to another day)…”), although here it just establishes when the action happened.

Why is 母 followed by に?

に marks the indirect object or recipient of the action.
In 母に電話をしました, 母 is the person you called (“to my mother”), so you need に to show “to whom” you made the call.

Why is 電話 followed by を?

電話 is the direct object of the compound verb 電話をする (“to make a phone call”).
を marks that you’re doing the action to 電話, i.e. performing the act of “making a call.”

Why is the sentence 電話をしました instead of just 電話しました?

The base expression is 電話をする, so you need を to connect 電話 and する.
Dropping を would make it ungrammatical here, because 電話 alone isn’t the verb—する is.

Could I say 電話をかけました instead of 電話をしました?

Yes. 電話をかける literally means “to dial/make a phone call,” and it’s very common.
電話をしました and 電話をかけました are nearly interchangeable in most contexts.

Why is there no subject in the sentence?

Japanese often omits the subject when it’s clear from context.
Here, it’s implied “I.” In English you’d say “I called my mother yesterday,” but in Japanese the “I” isn’t necessary.

Can I use お母さん instead of 母?

Yes. お母さん is the more polite/informal spoken form when talking about your mother.
母 (without お and さん) is neutral or used in writing and more formal speech.

Why is the verb in the polite past form しました rather than the plain form した?