If you don't have a single or few large files, but instead have many small files, you'll want to see how to tar and compress many small files. To compress file using gzip, type gzip file.name. That's it. This creates a file file.name.gz which should be much smaller than the original--how much smaller depends on the type of data in the file itself.
When you want to get your file back, it's also quite simple. First, ensure you have the space to do it... Then, simply type gunzip file.name, and the file will be decompressed, and put back to the file 'file.name'. You may encounter a warning or error though if you've since created a file by the same name.
If you only want to see the contents of the file briefly, you could also use the command gzcat file.name. This decompresses the file to the standard output (stdout) device, but leaves the compressed file alone. Oftentimes, this is used in conjunction with a pager to see the contents, such as gzcat file.name|less.