Elgato Game Capture HD has a Facebook Live Streaming option in the Live Streaming section.
The interface for Elgato Game Capture HD 2.5.2 for macOS is shown below, but the interface for Elgato Game Capture HD 3.5 for Windows is extremely similar.
Facebook - Setup with Elgato Game Capture HD
When you first start the software, Live Streaming is not yet setup.
Facebook Live Streaming - Sign In to existing account
To use Facebook Live Streaming, you must have a Facebook account.
Press the "+" button next to the Account option and select Facebook.
After you Log In, a new window will appear, telling you that Elgato Game Capture HD is requesting permission to connect to your Facebook account, including your public profile, events and videos.
Facebook will then ask you about who should see your posts.
Public - Everyone can watch
Friends - Only your Friends can watch
Only Me - No one can watch except for the creator
Custom - You can customize who can watch
Finally, Facebook will ask you for permission to manage and publish any Pages you are involved with, and access any Groups you manage.
Now your Facebook account is registered with Elgato Game Capture HD.
Then, come back to Elgato Game Capture HD and use the Log In procedure detailed above.
Facebook Live Streaming - Privacy and Category
At the bottom of the Live Streaming section, there is a small icon with a pair of tools on it. Pressing that button calls up a special Settings window.
Choose Privacy, so you can edit the settings.
To change the Privacy, choose between three options:
Only Me - No one can watch the stream except for the creator
Friends - Only your Friends can watch the stream
Friends of Friends - Only your Friends of Friends can watch the stream
Public - Everyone can watch the stream
For Category, you can't choose anything.
Facebook Live Streaming - Stream Bit Rate and Available Bandwidth
Before you start streaming, you can also adjust the bandwidth used to send data to Facebook.
Move the dial clockwise to increase the Bit Rate, which will make the video appear sharper.
Press the button on the bottom right part of the Live Streaming section to show the Settings again.
You have three choices for the Maximum Resolution:
If you are using 720p video, and you lower the Bit Rate a lot, Elgato Game Capture HD will switch the stream over to 480p. This is to maintain the highest visual quality for the chosen Bit Rate - HD video with a very low Bit Rate won't look that good.
You can also choose the Frame Rate:
The frame rate can have one of two values:
Please Note - you cannot use a Bit Rate that is higher than your available Upload bandwidth. Your Upload speed is determined by your Internet Service Provider (ISP).
You may have a fast Download bandwidth, like 10Mbps, but your Upload bandwidth is likely to be much lower, like 1Mbps.
To find out your available Upload and Download bandwidth, please use a service like http://www.speedtest.net
Facebook Live Streaming - Archive Live Stream
In the Live Streaming Settings, you can choose to Archive Live Stream Via Recording. It will be saved in the Edit section of the the Elgato Game Capture HD software.
You can also tell Facebook to Archive on Facebook (4 hour limit). Facebook save up to 4 hours of your stream.
Facebook Live Streaming - Start Streaming
Once you have entered your Facebook account, and have selected your Status and Bit Rate, then you can start Live Streaming.
Press the Stream button to Start and Stop streaming.
When you start Live Streaming, the Stream button will become bright green.
Next, Elgato Game Capture HD will look for a Facebook server. Facebook Live Streaming automatically selects the best server, and it can't be assigned manually. This process may take up to one minute, or more.
To go to your Facebook page, click on the Facebook logo next to the Stream button. Your Facebook page will open up in your default browser.
To go to your Facebook stream, click on the red ON AIR logo. Your Facebook stream will open up in your default browser.
Facebook Live Streaming - Live Commentary
If you'd like your voice over to appear on the stream, be sure to enable the Live Commentary feature in the Capture section of Elgato Game Capture HD.
For more information about the Live Commentary feature, please see this article:
How do I use Live Commentary with Elgato Game Capture HD?