To compress files use tar -czvf archive.tar.gz folder/, to decompress use tar -xzvf archive.tar.gz, where -c creates, -x extracts, -v shows progress, -f specifies file, and -z uses gzip compression.

To compress and decompress files in Linux using tar, use common options like -c (create), -x (extract), -v (verbose), -f (specify filename), and -z (gzip). For example: `tar -czvf archive.tar.gz folder/` to compress, `tar -xzvf archive.tar.gz` to extract.