ClearCase UCM and RTC: how do they get connected?

The details depend on whether or not you are using ClearQuest ... since you haven't mentioned ClearQuest, I'll assume you are not using ClearQuest.   In that case, you would be using the ClearCase Bridge to link RTC work items to UCM activities.   A couple of ways to navigate from a UCM activity to its associated RTC work items would be from the UCM activity context menu or from the UCM activity property page.  To navigate from an RTC work item to its associated UCM activities, you would use the links tab of the RTC work item.   Details can be found at:
https://pic.dhe.ibm.com/infocenter/clmhelp/v4r0m2/index.jsp?topic=%2Fcom.ibm.team.connector.scm.cc.doc%2Ftopics%2Fc_bridge_intro.html

Or are you interested in the API that would let you programatically perform this navigation?

Hi,

You can find videos about how to use ClearCase bridge from this article:
 Rational Team Concert and Rational ClearCase - Integration Cookbook

If you are looking for a way to retrieve it programatically, the link from work item is available via OSLC, and the link from UCM activity is available by cleartool describe ( your VOB has to be feature level 7 or higher in order to see the link in cleartool describe ) .

The sample code of accessing CC Bridge OSLC link is available at:
Using ClearCase triggers to implement ClearCase Bridge capabilities in Rational Team Concert or
Migrating from a ClearCase-ClearQuest integration to a ClearCase-Rational Team Concert integration