The version of tar in most Linux distributions supports gzip compression. This means that a gzipped tar file can be extracted in one simple command.
To extract the archive filename.tar.gz into the current directory:
tar xzf filename.tar.gz
If this fails, the version of tar may not support gzip compression. In this case, you can use the traditional two-stage command:
gzip -dc filename.tar.gz | tar xf -