Learn Hardcore Japanese: sigoto ni ha keiken ga hituyou desu.

Here に marks the target or “scope” of the necessity (“for the job”), and は turns that whole phrase into the topic (“as for the job…”). Put together, 仕事には means “as for this job” or “for the purposes of this job.”

Why is が used before 必要? Can’t we use は instead to mark 経験?

が here marks 経験 as the grammatical subject (the thing that is necessary). If you used は (経験は必要です), you’d be shifting the topic to “experience” (“as for experience, it’s necessary”), which changes the nuance. が keeps 経験 as the focus of the predicate 必要です.

What kind of word is 必要? It doesn’t look like a verb.

必要 is a na-adjective (also thought of as a noun meaning “necessity”). When you attach です, it behaves like an adjective:
• Literal: 経験が必要だ (casual)
• Polite: 経験が必要です

Do we have to say 必要です? Can we drop です or change it somehow?

In casual speech you can say 必要だ. In written or polite contexts, you use 必要です. You can also make it negative:
• 必要ない (casual negative)
• 必要ありません or 必要じゃありません (polite negative)

Couldn’t we use the verb 要る (“to need”) instead of 必要です?

Yes. You can say 仕事には経験が要る in casual speech. But 要る is a plain u-verb and sounds more colloquial; in business or polite contexts, 必要です is more common.

Why isn’t 経験 marked with を as a direct object?

Because 必要 is not an action verb that takes an object. It’s a descriptive predicate (na-adjective), so its “subject” (what is necessary) takes が, not を.

How would I turn this into a question (“Is experience necessary for this job?”)?

Simply add か at the end:
• Formal/polite: 仕事には経験が必要ですか？
• Casual: 仕事には経験が必要？

How can I say the negative (“Experience is not necessary for this job”)?

Replace です with a negative form:
• Polite: 仕事には経験が必要ありません。
• Casual: 仕事には経験が必要ない。

Can I move 仕事には somewhere else in the sentence?

Word order in Japanese is somewhat flexible, but the topic phrase 仕事には usually comes near the front. If you push it too far back, it sounds odd. The most natural is:
• 仕事には経験が必要です。