I assume you installed SketchUp correctly, but just to make sure, the process is:
Download the installer .dmg file
In your download folder, double-click the installer .dmg to mount and open it. A disk image icon should appear on your desktop and then the installer starts to run.
In the dialog that pops up, drag the SketchUp icon onto the Applications Folder icon, as indicated by the large gray arrow. You should then see a message about copying files.
When the install completes, the dialog should close. If it doesn't, click the red button to close it.
Right-click and eject the .dmg from your desktop.
SketchUp should now be installed in your /Applications folder. Run it from there. DO NOT attempt to run it from the .dmg image - that will cause errors and crashes!