DCR files are movies created with the Adobe Director program. Without Director, you cannot do much with a DCR file. If you want to share a DCR with friends who do not have the program, you'll need to convert it. ShockWave Flash (SWF) is a popular video format that most people will be able to play. Unfortunately, because DCR is unique to Director, you cannot convert directly on a Mac. You have to capture it first and then convert it to SWF.
Download or purchase a video capture application. There are several such programs for Mac. One popular choice is Snapz Pro X (see Resources), but do some research to find the one best suited to your needs. Whichever you choose, be sure it can output in SWF format. Note that it does not need to say it is DCR-compatible (none are).
Open the video capture application.
Select "Director" as the program to capture. Director is the only software that can create and play DCR files.
Open the DCR file in Director.
Begin the capture in your video capture application. As soon as you do, press "Play" in Director.
Stop the capture when the DCR movie finishes.
Save the capture. Select "ShockWave Flash (SWF)" as the output format.