First and foremost, Bing and Google are your friends. Make it a point to spend time with each in your quest for knowledge.
Suffice to say, there is TONS of info related to what you asked, here's some info to get your started:
What's a .dmg?
A .dmg file is an Apple Disk Image. Basically, it is a file that looks and acts like a hard disk or a CD/DVD. The same way you can take a DVD of Adobe Photoshop and insert it into your Mac and it opens, a .dmg will do the same thing. Another way to look at it is being a "virtual" disk.
What's a "zip" file?
A zip file is a file that has been compressed (made smaller) to save space and make it easier for transport (like email). It can be one file, or many files in a zip archive, but the key here is that it is compressed.
What's a "tar" file?
A tar file or more commonly known as a Tarball is a collection of files into a single archive. An easier way to think about this is if you had a collection of music all sorted by album. If you get a big safe crate to store every one of your albums in, then the crate would be your Tarball.
Conveniently, you can combine the compression and tarring of files so that you end up with a compressed archive. These will be archives that look like .tgz In this case it was "tarred" and "zipped."
As for "what do you do next" that comes down to what do you want to accomplish?
For now, so you can get a better understanding of Unix and how it relates to OS X, there are books like Learning Unix for OS X and YouTube Videos
I hope this is answer was able to get you started off in the right direction.