Rift Settings

In game video settings have a large impact on framerate, as would be expected. Try decreasing your settings using the top slider in the advanced video settings. If your framerate does not change significantly when changing from high settings to low settings this generally indicates a problem external to rift, most likely a driver issue. In this case, ensure you are running the latest drivers (see below).
Certain video settings have a much larger framerate than others. Some examples of these settings are: antialiasing, shadows, and ground clutter. Disabling vertical sync will also result in a framerate increase. Each setting has a tooltip which indicates if that option is especially expensive, as well as whether that setting requires CPU or GPU processing. If you know one aspect of your system is weaker than another, you can disable specific settings to tune your performance for your hardware configuration.
Resolution also has a large impact on framerate. Attempt to lower your resolution and see if your framerate improves. If it does not, that indicates you are CPU bound, and therefore should reduce settings which are listed as CPU intensive. If framerate does increase, you may either keep the new resolution, or go back to your original resolution, and try lowering settings which are listed as GPU intensive.

Hardware Specific Performance

AMD is actively releasing new drivers which often contain Rift specific fixes. Updating to the latest driver may result in significantly improved framerate.
AMD has also recently released a new application profile. Downloading and installing the latest Rift application profile may result in significantly improved framerate. Note that this profile is not just for CrossFire, it may result in improvements even if you do not have a CrossFire setup.
Ensure "Anti-Aliasing" and "Anisotropic Filtering" are set to"Application Controlled" in the Catalyst Control Center.
Disabling "Morpological Filtering" in the Catalyst Control Center will result in improved framerates.
Disabling "ATI Overdrive" may result in increased framerates in some configurations.

Ensure “Power Management Mode” is set to “Prefer Maximum Performance” in the NVidia control panel.
Ensure "Anti-Aliasing" and "Anisotropic Filtering" are set to"Application Controlled" in the NVidia Control Panel.
Ensure "Transparency Anti-Aliasing" and "Ambient Occlusion" are set to"Off" in the NVidia Control Panel.

General Performance

Any programs which use flash (for example a browser playing YouTube) can incur a significant framerate hit in game. The reason for this is if flash hardware acceleration is enabled, it will cause certain video cards to downclock to 400 MHz, resulting in much lower in game framerate. This will apply as long as the flash application is open, regardless if it has focus, the video is paused, etc.
To fix this issue, either close any programs which are running flash, or change flash to disable hardware acceleration (when mousing over flash application: right click...settings...uncheck "Enable Hardware Acceleration").

Background Programs
Background programs can also have a significant impact on your framerate, if they are taking up large amounts of your CPU. Ensure you have no other programs running. This includes: antivirus, automatic updates, video and music players, etc.

Window Postioning/Mode and Multiple Monitors
Fullscreen mode will generally result in higher framerates than windowed modes. Beyond that, while in windowed mode a couple things can severely hurt in game framerate. Ensure the client window does not span multiple monitors in any way (even just an edge hanging onto another monitor). The impact of this is significantly greater when using multiple video cards to drive different monitors. Also ensure that the circular Windows start button on Vista and Windows 7 is not overlapping the client window, as this can have a significant effect on performance as well.
When running with multiple monitors, ensure that all monitors are running the same color depth (for example 32-bit).

Overheating can manifest in several ways including degrading framerate, system shutdowns, and intermittent hitches in performance. This is generally most common in systems which have been overclocked, however it can occur on stock systems as well in cases of fan failures, etc. There are many utilities which can be used to monitor the temperature of your hardware. One such example is: http://www.cpuid.com/softwares/hwmonitor.html.

Power Saving/Hardware Throttling
Many hardware configurations support power saving modes in which the hardware is run at lower frequencies than it is capable of to conserve power (for example AMD's Cool and Quiet). These settings are generally changed in the BIOS, refer to your motherboard or system manual for information on how to change these.
Both Vista and Windows 7 also have additional otions for power management. In Vista, under Control Panel->System and Maintenance->Power Options, select High Performance. On Windows 7, Control Panel->Hardware and Sound->Power Options, select High Performance.

Underclocked Hardware
Underclocked hardware is generally caused by using newer processors in older motherboards which do not recognize it, or harware being set up incorrectly. These issues can generally be resolved by updating your BIOS. Refer to your motherboard or system manual for more information on how to do this.

Sound Driver Settings
Disabling any active sound post processing effects can result in improved framerates.

Hardware Limitations

Rift utilizes both the CPU and the GPU extensively. Running at high settings requires both components to have sufficient processing power, or else your framerate will become bottlenecked by the slower component. See above for more information on how to tune settings for a specific configuration.
Rift also provides an option specifically for the support of low end and integrated video cards. If you are running a video card with limited processing power, try enabling the "Low Quality Renderer" and restart the client.