At least for now, you need to use the Windows App to easily get a list of email addresses. Select Tools > Gather E-mail Addresses and Textible Phone Numbers to bring up a dialog that will guide you through the process. This tool is the best option if you want info for all households with a particular status, or you have linked email and phone records to specific members.
If you have not linked records to specific members or need email addresses for a particular club (or filtered in any way), you can use the Clubber or Leader grids to select the members you need info for, then right-click to copy the primary email addresses or textible phone numbers for selected members.
Note: The Web App does not yet allow you to change the primary email address or phone number after the initial creation of a member, so if you need to gather this information from your database, you'll want to first make sure the correct records are set as primary by using the Windows App You can easily see all of the primary information within the Clubber and Leader grids, as long as the Household Info's Primary Phone and Primary Email columns are showing. To change the Primary setting, double-click a member to bring up their Member Dialog, then double-click in the Contact Info area to bring up the Contacts dialog. (This is also where you can link records to a member in order to use the filter options within the Gather E-mail Addresses and Textible Phone Numbers tool.)