Extract data to another computer
There are a few ways to do this, some easier and safer than others.  You could mess around with detaching and attaching, but I will never recommend that solution for normal cases like these.  Since you have your database on SQL Server Express Edition, then it can't be larger than 10 GB.  It'll be a quick and painless process to just backup the database, and jump over to your other machine and do the restore.

The Import/Export features aren't worth the hassle in this case.  Backup and restore would be the easiest route.

If you're looking to only move a certain amount of data (say, a handful of tables), then I'd just as soon generate the scripts (for data and schema if that's desired).  You can do this by right-clicking the database in Object Explorer, Tasks, and Generate Scripts.  You'll have numerous options for this task, and you can specify a subset of objects to script out.  Then you could run that script on your destination instance.

Just to reiterate, I'd do the backup/restore for the entire database copy, or generate scripts for a subset of objects.