How do I find out the last login time of a user when they log into their Gmail account?
I believe when you say "their Gmail account" you actually mean your account. You cannot find out about other users last login time or activity.
To see the latest activity of your Gmail account
On the main screen find at the far bottom right part of the page the
Detailslink and click on it.
A pop-up window will appear with the account's latest activity.