Flimsily Constructed Cardboard Box

Quick demonstration

Firefox includes a feature that lets you use multiple identities (multiple accounts) on one site, with each account in a distinct, colour-coded "container". What this means for NationStates is that you can be logged in to multiple nations in different tabs all at once, without having to switch between them. This allows to greatly speed up card farming, as switching between nations can take a considerable amount of time. Of course, the more farming puppets you have, the greater the time savings.
In essence, containers can be thought of as if you're using a different browser (or private browsing) for each nation, but all within a single browser instance.
This feature stems from Firefox' desire to be a privacy-focused browser. So far, it is exclusive to Firefox, and won't work in Chromium-based browsers (Chrome, Edge, Opera...).
One of the many extensions leveraging the power of Firefox' containers is Containerise, which lets you automagically open a tab with a different, logged-in nation (without having to log out from all of your other ones) by simply clicking a link.

TL;DR: Containers are a Firefox exclusive feature that enables you to be logged in to multiple nations without having to switch and relogin.

TL;DR: Install Firefox and Containerise.

I've created a python script that can automate this step for you (along with some other features).

This is the most confusing step of all. Containerise uses a special syntax, Regex, to choose when to switch to a different "container" (nation).
There's two main ways in which you can configure the extension to switch to a nation: nation=puppet or container=puppet.

If in doubt, nation=puppet is usually easiest for beginners and will work out of the box.
You will have to generate a rule for each puppet, like this:

The part before the comma is the puppet's name, all lowercase, spaces replaced with underscores. The part after the comma is any name that uniquely identifies your puppet (purely cosmetic, but it has to be unique — I recommend just using the puppet's name). The easiest way to generate these rules is with a spreadsheet.

Having done this, click on the Containerise extension's button (four colourful squares).

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TL;DR: Read the damn step, it's important. Or use the python script.

Note: you don't need to follow this step if you're using the python script.

It's a good idea to generate clickable links to each of your nations, so that it automagically opens a new container-tab. If you don't want to use the script from the previous step, use a spreadsheet. You can also add additional links that redirect you to any NS page, like your puppet's issues or it's deck page.
The links should be in this format:

• container=puppet:
  https://www.nationstates.net/container=my_puppet_1
  Issues link: https://www.nationstates.net/container=my_puppet_1/page=dilemmas

• nation=puppet:
  https://www.nationstates.net/nation=my_puppet_1
  Issues link: https://www.nationstates.net/nation=my_puppet_1/page=dilemmas
  

TL;DR: Too lazy to read an optional step? Your loss.

1. Open a new container-tab according to the rules format you chose:

   • container=puppet:
     https://www.nationstates.net/container=my_puppet_1

   • nation=puppet:
     https://www.nationstates.net/nation=my_puppet_1
     

2. Click the Login button

3. Enter your credentials and click the Stay logged in/Remember me checkbox.
   (If you don't you'll have to login next time — that defeats the purpose of containers)

4. Click the Log in button
   

TL;DR: You'll figure this out sooner or later. Or you could just read the 84 words.