Erik Erskine - Help! This composer stuff is confusing

Drupal 8 makes use of Composer - a tool widely used in PHP for managing dependencies.

Composer's introduction hasn't been plain sailing. There are now several different ways you can install Drupal, and a concern that this is one more barrier to entry for new Drupal users.

We'll try to address some of the confusion surrounding Composer, by answering these questions:

What problem does Composer solve? Do we even have that problem?
Drupal's documentation mentions "drupal/drupal" and "drupal-composer/drupal-project" as two alternative ways to install it? What's the difference? Can't you just tell me which one to use?
The installation instructions I see talk about "8.x-dev". What if I don't want to use a dev version?
I'm not very familiar with the command line. Is that now essential for Drupal development?
We'll also look at some practical tips if you decide to use Composer:

Should I use exact versions or patterns for module dependencies?
Do the dependencies go in the code repository?
Do I need to run composer on my server?

Drupal is a registered trademark of Dries Buytaert.