What is Towny?
Towny is a Vanilla-esque Survival server that gives you the ability to claim land, invite other players as Residents of your land, and give them control over "Plots". In other words, as the name implies, it allows you to create Towns. Alternatively, you can join an already existing Town and take part as a Resident of the Town if you'd prefer not to manage an entire Town.
What is a Town?
At its most basic, a Town is land claimed by a player. Towns can include various types of Plots, such as Farm Plots, Inn Plots, Resident Plots, etc. Different Plots serve different purposes. For example, a Farm Plot allows all Residents of the Town to plant and harvest Crops, Trees, and Animals in that plot.
Towns consist of a Mayor; who owns the Town, possibly Assistants; who have some control over the Town, and Residents; who reside in the Town and benefit from its prosperity.
Mayors can give or sell Plots to Residents, who can then build within the Plots they own. Mayors may collect daily taxes from Residents who own Plots within the Town.
How to Create a Town
First, pick a spot you like that isn't too close to another Town. The command "/wild" will help a lot here as it will teleport you somewhere random. If you don't like the spot it teleports you to, or there's a Town nearby, simply continue using the command until you find a place you like.
Once you've found a nice place to live, you can create a Town there using the "/tgui" command. This will open a Menu with various Icons representing the different Towny functions. Click the "Town" icon to access the Town functions. From there, click the "New Town" icon and enter a Town name. This will automatically claim the chunk you're standing in as your Town's "Home" block.
As Mayor of the Town, you can add Residents as Assistants or Helpers through the Town Menu. Assistants are exempt from Daily Tax, have access to claiming land for the Town, adding Residents to the Town, Switching Town options, controlling Plots, toggling the Public status of the Town, and can add other Residents as Helpers. Helpers have access to Switching Plot options in the Town.
How to Expand a Town
To expand your town, you need to claim more "Townblocks". Townblocks are just chunks that you can claim for your Town. To claim a Townblock, either use the "/tgui" command again and select the "Town Claim" icon to claim the chunk you're standing in or refer to the commands here for more types of claiming: http://towny.palmergames.com/towny/towny-commands/.
The more Residents you have in your Town, the more Townblocks you'll have to claim. You can also purchase "Bonus" Townblocks through the "/tgui" menu.
To add Residents to your Town, you can invite them through the "/tgui" menu. They will then have to accept the invite to join your Town.
Optionally, you can also set the Town as "Public", allowing anyone to join at any time through the "/tgui" menu under the "Town" icon.
You can only claim land connected to land you already own, unless you're claiming an Outpost.
An Outpost is basically just a plot of land away from your Town. This gives you the ability to claim areas you'd like to own that aren't close to your Town. You can claim an Outpost using the "/tgui" menu and, in the same menu, you can also teleport to your Outposts.
As Mayor of a Town, you can put Plots of land up for sale that your Residents can then purchase. You can do this through the "/tgui" menu under the "Plots" icon. You can also set the options for the Plot you're standing in through the Plots Menu, such as Plot Type or Plot Permissions.
As a Resident of a Town, you can purchase Plots that are for sale through the same menu. You can build in Plots you own and change various permissions through the Plots menu.
Plot Permissions can be set to allow or deny Allies from accessing or building in the Plots. This can be useful for collaborating between allied Nations.
What is a Nation?
A Nation is a collection of Towns. The owner of a Nation is that Nation's King and can set daily taxes for the Towns that belong to it.
Nations can ally other Nations and take part in the weekly War event. They also have their own Banks.
Allied Nations are useful for preventing friendly-fire (PvP) between allies and allowing allied players to build or access Town Plots where the permissions are appropriately set.
How to Create a Nation
To create a Nation, you must first own a Town. Then, in the "/tgui" menu under the "Nation" icon, click "New Nation" and give it a name. Your Town then becomes the Capitol of the Nation.
You can then invite other Towns into your Nation through the Nation menu.
As King of the Nation, you can collect daily taxes from the Towns and ally your Nation with other Nations. You can assign Residents as an Assistant or Helper through the Nation menu. Assistants have access to add Towns to the Nation, add other Nation Residents as Helpers, Ally other Nations, or declare other Nations as enemies. Helpers have access to adding Towns to the Nation.
More Detailed Information
This was just a basic overview of Towny. For more detailed information on all the Towny features, please see: http://towny.palmergames.com/towny/757-2/