Learn Hardcore Japanese: watasi ha keisatu ni denwa wo simasu.

は is the topic marker, indicating what we’re talking about (here, “as for me”). が is the subject marker, often used to introduce new information or emphasize the subject. In this sentence, the speaker is already known or assumed, so は is natural to set 私 as the topic.

Why is the particle に used after 警察?

に marks the indirect object or the target/recipient of an action. Since you’re “calling the police,” 警察 is the recipient of your call, so it takes に: “to the police.”

Why is 電話 marked with を?

を marks the direct object of a verb. Here the action is “to make a phone call” (電話をします), so 電話 is what you’re doing and takes を.

What exactly does 電話をします mean? How does it differ from 電話します or 電話をかけます?

電話をします literally means “to do a phone call.”
電話します is a slightly more contracted form; it’s understood the same way but a bit less explicit about を.
電話をかけます uses かける (“to dial/attach”), which is more specific to “dialing” or “making” the call. All three are common, but 電話をします is perfectly natural and very common in spoken and polite Japanese.

Can you omit 私は here?

Yes. Japanese often drops topics/pronouns when context is clear. If it’s obvious who is calling, you can say simply 警察に電話をします or even 警察に電話します.

Why does the verb come at the end of the sentence?

Japanese is an SOV (subject-object-verb) language. The verb always comes last, so you list the topic/subject (私は), then any objects or indirect objects (警察に電話を), and finish with the verb (します).

Why use します (the polite form) here, and what would an informal version look like?

します is the polite present/future form of する (“to do”). In casual speech you’d use する, so the sentence becomes 私（は）警察に電話をする. The meaning stays the same; the register just becomes more familiar.