Note: iCalendar is an IETF standard (RFC 5545) and not to be confused with Apple iCal.
Note: This article explains how to subscribe to and publish iCalendar feeds, not how to export and import iCalendar files, which would be of limited use.
Doodle to iCal/iCloud
With your browser, go to https://doodle.com/account#calendars and copy the link from the “Doodle calendar feed (ics)” section, e.g., http://doodle.com/ics/mydoodle/c441dlaaezup2c1e78tylnjulce5c5xs.ics.
In Calendar (Apple iCal), choose File > New Calendar Subscription..., paste the link copied above, and click Subscribe.
Select an Auto-refresh rate (e.g., daily) that reflects how often you use Doodle and the Location and click OK. The Location determines whether all your Calendar apps on all your Apple devices are subscribed to the Doodle feed (Location = iCloud) or only the one currently in use (Location = On My Mac).
iCal/iCloud to Doodle
Requirement: iCloud needs to be enabled for Calendar (Apple iCal).
For each Calendar (Apple iCal) calendar that you would like to view within Doodle, follow the instructions at http://support.apple.com/kb/ph2690 for publicly sharing a calendar. Have Calendar send the link to your own e-mail account, copy it directly, or right-click the calendar name and choose Copy URL to Clipboard, e.g., webcal://p09-calendarws.icloud.com/ca/subscribe/1/SrehsOxFR6x8mTRZFkCjQB1QDrnVOQQ5vDZh9ZoqpoKZB3vmg2RN2rasPDxM6JTK9KgysAjpLUgYH4nqZqwNRQ2L0qQ3zFLCoGm_FfzQ1po.
With your browser, go to https://doodle.com/account#calendars, click on "ICS feed".
Now paste the link copied above into the “Add a calendar feed by URL” field and click "Add".
Afterwards, remember to update your MeetMe settings at https://doodle.com/account#meetme if you have a MeetMe page.