Action Details
Requirements and how-to articles for Discord's action:

Servers on Discord act as a hub of communication for everyone who is a member of that server, with both text and voice communication channels available.

You need this to get it done:

Server Name
The name of your server (can include spaces, symbols, emoji etc.)
Server Region
Choose your server region. The current regions available to select from are: Brazil, Central Europe, Hong Kong, India, Japan, Russia, Singapore, South Africa, Sydney, US Central, US East, US South, US West and Western Europe.
Server Icon
The icon that represents your server.
File format: .jpg/.jpeg/.png/.gif
Minimum dimensions: 128 x 128 pixels (recommended at least 512 x 512 pixels) (will be automatically cropped to a circle)
Invite Users
Invite fellow Discord users to join your server. You can either send individual invites to people on your friends list, or copy and paste a server invite link for people to click if they want to join your server.
Create Channels
By default your new server will already have one text channel and one voice channel, but you can have as many as 500 channels (although you most likely won't need anywhere near that many!)
Many Discord servers have a "welcome" channel, a channel which lists the rules of your server (generally this is a channel with one message from an admin/moderator with the rules, and then no one else has permission to post in that channel, to avoid the rules getting buried under lots of messages) and then channels for different topics (e.g. general chat, fan art, memes, etc.)
Set Up Roles
Servers with a lot of members usually have a role hierarchy (e.g. admins, moderators, players, etc.) Each role has different permissions (e.g. a moderator can edit/delete messages or kick members whilst a player cannot) and helps to keep the server running smoothly. You can also create channels which are only accessible by some roles but not others (e.g. a channel for admins and moderators which cannot be read by players.)
Server Banner Background (if verified)
If you have Verified Server, you can upload a Server Banner Background which is displayed in the top left corner of your server, above the list of channels.
Minimum dimensions: 960 x 540 pixels
Aspect ratio: 16:9
Discord recommends keeping the top 48 pixels of the image simple and without any busy imagery, as this is where the name of your server will be displayed.
Requirements missing or found errors? Report

How-To Articles
A list of useful links for you:

Discord Support - How do I create a server?
Official guide to creating a server on Discord.
Discord Developer Portal - Vanity Perks (Server Banner Background)
Official specs for Server Banner Backgrounds for Verified Servers.
Discord Developer Portal - Channel Documentation
Official technical documentation regarding Discord channels.
Discord Support - Advanced Community Server Setup
More in-depth official information on setting up a server on Discord.
Link missing here or found errors? Improve How-Tos