To get going quickly, you will need several things. A computer with speakers or headphones, and the right software designed with music production in mind.
--------------------------------------------------------------------------------
The Computer
All modern computers and laptops are powerful enough to run music production software today. (By modern, we're talking anything made in the last 5 or 6 years).
So long as your computer has some speakers or headphones, you're good to go!

Mac vs PC
Regardless of what others tell you, it does not matter whether you use a Mac or PC. The majority of popular creative software is available on both platforms, and operate identically across both platforms too.
Which one you choose and use should be based on your understanding of the platform you know best. This will help you focus upon making music and not on the technical sides of computing systems. If you're on a Mac, stay with the Mac. If you're on a PC, stay with the PC.
It is a myth that Macs are better than PC's for creative tasks, they are simply different. Each platform has benefits and restrictions, thus, neither platform is better outright. Which platform is more suitable for you depends entirely on the purposes you need to use the computer for. It also depends on your general level of knowledge regarding using computers and your 'workflow' preferences.
--------------------------------------------------------------------------------
The Software
Music software ranges from simple audio recorders to 'modular' environments allowing multiple devices to be connected in complex ways. The majority of producers use 'sequencing' packages often refered to as 'DAWs' to record and arrange their music.
What is important is that you can understand how it works quickly and easily. By starting with simple programs you'll learn the basics quickly and have fun doing it. As soon as you're confident with the basics, it is easy to progress to more complex programs.
Sequencer packages and 'DAWs'
Sequencer packages today are generally refered to as 'DAWs', an acronym for 'Digital Audio Workstation'. They allow users to record and arrange audio, and to control to midi devices and 'plugins'.
Plugins are a type of software that add enhanced capabilities to a sequencer package, most often in the form of extra synthesisers or effects. While simpler music software packages won't always support plugins, almost all the advanced ones do. It is worth noting that plugins can often add a layer of complexity to using music software, so if you are just starting out, it may be prudent to stick to simpler programs that come with their own built in synths & effects.
Samples & File Formats
Music software can usually save two kinds of files, audio files and 'project' files. It is worth noting that there is a fundemental difference between audio files and project files.
Audio files contain audio data and are used to record and playback music or sound. They can be played upon digital players such as iTunes or Windows Media Player, and also on CD or DVD players once burnt to disk. Project files are the work files each program uses to save recording sessions for continuation at a later date. Project files can only be opened using the program that created them.
Most music sequencing programs can read and write the .wav format of audio file. More often than not, they can usually read and write other audio file formats such as .aiff, .mp3 and .flac too.
--------------------------------------------------------------------------------
Choosing the Right Software
When deciding which software to use, you should consider a few things first.
1> Your willingness to learn and to seek out new methods of creating music.
2> Your knowledge level regarding music and music production.
3> Your level of patience with computer programs.
4> Your visual preferences regarding the colour theme of a program and the layout of its controls. (Each program has its own visual style and workflow, and for most music producers this is the deciding factor in which programs they use regularly).
Easy-to-use Music Software
If you are completely new to making music on a computer, the following programs are a great place to start. They are fairly easy to learn and won't confuse you with unneccessary features. Many programs also come bundled with premade music loops and sound samples. This can be great for quickly building new tracks from scratch.
(The first 3 programs come bundled with many premade loops and sounds to get you going).
1> eJay
2> Music Maker
3> Garageband
4> Acid Pro
5> EnergyXT
6> Podium
7> Tracktion
Advanced Music Software
If you already have some experience in creating music, you may prefer to choose a more advanced program from the outset. The following programs all share very similar capabilities. The main differences between the following programs are in the layout of the Graphics User Interface and the methods used to perform various production tasks. As we all have a different sense of asthetic and logic, you may find one program is easier to use than the others. It is really important to try for yourself as many programs as possible, this way, you'll discover quickly which one is the right one for you.
Reaper
Logic
Ableton Live
Reason/Record
FL Studio
Cubase
Sonar
Pro Tools
Digital Performer
Samplitude
Audition
Renoise
--------------------------------------------------------------------------------
More Resources
01 - A completely free music studio that runs off a USB stick and has everything you need to make music quickly
02 - Discussion on the best DAW to get started with
03 - Discussion about starting out in general
04 - More about what software is good for starting out with
05 - Discussion on different programs
06 - Recommendations on Soft Synths
07 - More talk about Soft Synths
08 - Discussion about who uses what software
09 - What is the best music software to use?
--------------------------------------------------------------------------------
As ever, if you have your own tips to share or any suggestions on improving this article, post 'em below!

Patrick