Hardware

Needed

Raspberry Pi
MicroSD Card 4GB or larger
USB Keyboard
USB Power Supply and cable with micro USB Connector
Display (Composite or HDMI)
Display cable (Type of cable depends on monitor)
MicroSD Card to SD Card Adapter (Needed only if your PC has a SD Card Reader but not a MicroSD Card Reader)

Nice to Have

Raspberry Pi B+ Case (Note cases for other models may not work)
WiFi module or Ethernet Cable

Steps

Download the Raspbian Image from http://www.raspberrypi.org/downloads/ (As of this post, the file is 2014-06-20-wheezy-raspbian.zip)
Unzip the Raspbian Image File
Follow the instructions at http://www.raspberrypi.org/documentation/installation/installing-images/README.md for your operating system. I will be using Windows and will mirror the steps from the installation instructions page

Windows Installation

Insert your MicroSD card into the card reader on your PC (NOTE: You may need a MicroSD to SD Card Adapter)
Download the Win32DiskImager utility from http://sourceforge.net/projects/win32diskimager/ (As of this post, the file is Win32DiskImager-0.9.5-install.exe)
Install the Win32DiskImager Utility by double clicking the downloaded file
Click on the “Next >” button on the setup wizard
Select the “I accept the agreement” radio button and click the “Next >” button
Click the “Next >” button on the destination location dialog
Click the “Next >” button on the Select Start Menu Folder dialog
If you do not want a desktop shortcut, uncheck the “Create a desktop icon” checkbox
Click the “Next >” button on the Select Additional Tasks dialog
Click the “Install” button on the Ready to Install dialog
Wait for the installation to complete
Click the “Finish” button on the Completing the Win32DiskImager Setup Wizard dialog
It is possible that you may see the following error message
If you see the error message above
1. Click the “OK” button
2. Right-click on the desktop shortcut and select “Run as administrator” from the pop-up menu
3. When the User Access Control dialog is displayed, click the “Yes” button
The application is now open
Click the folder icon and select the Raspbian image file downloaded earlier
Select the drive letter for your MicroSD Card
WARNING: Be very careful to select the correct drive letter as the utility will erase all data on the drive! You have been warned!
Click the “Write” button
Click the “Yes” button on the confirmation dialog

If you see the following error (), check that there are no open Explorer Windows or other applications attempting to access the SD Card

If you see the following error, check the write lock switch on the MicroSD Card Adapter

Wait for the process to complete
When the process is complete, click the “OK” button
The main window will display the status as “Done.” Click the “Exit” button to exit the utility
Eject the MicroSD Card