How can I know when a computer that is missing gets logged into?

You can't

When you say it's missing, can you be more specific? Is it in Active Directory? Can you access it on the network? Is it attached to a domain?

Regards
Alex

Sorry Alex. a teacher who is here said her laptop was missing. I asked her to send me the name which she has not yet done. When she gives me the name, I want to ping it so that when the next time the laptop is logged onto, I will get an alert that this laptop is now logged on.

$sendMailArgs = @{
	From = 'Change this to your from mail'
	To = 'put in your email'
	Subject = 'computer online'
	SmtpServer = 'put in your mail server'
	BodyAsHtml = $true
	Priority = 'High'
Send-MailMessage -Body "machine online" @sendMailArgs

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Have that as a start up script and then have this one machine in the scope of the group policy

Oh yea. They are encrypted. Thanks. This will be good.

If it's suspected stolen, disable the computer account. Then check the event security logs for failed logons.

If you want a more specific alert to be sent if someone tries to connect it back to the network, that would require more than a command, it would need third party software.

Brian, loved this answer. That I can do. Thanks again.

I will call this lost computer the "foreign computer".

Here is what I see as concerns regarding the foreign computer:

One is that it's been stolen.

One is that it may have sensitive data on it.

One is that it can log into YOUR network.

Aside from the hardware being stolen, the sensitive data is protected from hard drive snooping if Bitlocker or some other encryption method was in use.  This only helps if Windows can't be logged into.  So that ability would be a key question.  Was the login information written on the case in bold permanent marker ink?

As far as logging into your network, you've received some good advice regarding how to detect that.  But how likely is that?
Was the organization's identity made available somehow?
Finding your network could be looking for a needle in a haystack.  Or not ........