Did you download from here?

Open the terminal and navigate to the download location (may be cd /home/user/Desktop or /home/user/Downloads). Then, unpack the compressed file with this command:

tar xjvf sunbird*.tar.bz2

Then, navigate to the directory that was formed (cd /home/user/Downloads/sunbird/) and start the sunbird script.

./sunbird

If you want to run it in the background, use the & key like this:

./sunbird &

If you get a permissions error, then run this command before trying again with ./sunbird

chmod u+x sunbird

You can also do this with the Archive Manager by extracting the folder and running the same sunbird script.