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I am a little confused about the purpose of a spousal IRA.
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If you earn $4000, you're allowed to put $2k in an IRA and your wife is allowed to put $2k in her IRA, whether or not she earned income. The "spousal" part just indicates that the owner doesn't have to have earned income to contribute.

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If I am the only wage earner in the family, do I have to open a spousal IRA for my wife in order to put money into it?
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There's no requirement that your wife have an IRA, nor that anything be contributed if she does.

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Can she open an IRA while she is still working and continue to put money into that account when she is no longer receiving earned income?
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Yes.

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I believe that we can contribute $2000/year for her, regardless of employment status, but how do the mechanics of this work out?
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Mechanics are no different based on employment status. The custodian of the IRA doesn't know or care about your wife's employment status.