|(I started typing this post before there were any other responses.)|
I don't use Outlook Express, but these things I have found applied on other people's computers who were using Outlook Express I have worked on.
You can use the same user name / password you use on your desktop, for your same email account in Outlook Express itself, on the laptop.
For that matter, you can do that with any email program on any computer, as far as I know.
However, when the computer is connected to the internet (can connect to the internet in the background), Outlook Express is usually set by default to check for email when you first open it, and check again every so often while you're using it, and it will by default download any new email found to whatever computer you're using at the time automatically.
You can change default settings in Outlook Express, which I don't know much about,
or for any email program, if an email was downloaded to one computer and you also want it to be on another one, you can re-send that particular email to your own email address, then exit your email program on that computer, and have the email program download that into your email program on another computer.
The latter works fine if you only need to have an occasional email on two of your computers.
There's lots of help on the Microsoft web site in the Outlook Express support, and there's lots of help for it on the web as well.