After you've assigned an app to one of your spaces, and you select it in the Application Assignments list, the space it resides in becomes highlighted in the graphical representation above the list. The highlight moves to whichever space you assign in the list, and it will change as you move between applications in the list.

When you are setting up your spaces and you want to assign several apps to one of your spaces, just add the first app and assign it to the desired space (the space is now highlighted). If you now click on the plus sign to get the Open dialog, you can choose multiple apps by command-clicking the ones you need.

When you have selected all the apps you want to reside in the highlighted space, just click Add, and all the selected apps will be assigned to that space. Just repeat the process for each space, and you're done.