I've been using Open Broadcaster Software (OBS) to record out of my webcam, the same webcam as yours, in fact

The program is not necessarily designed for it, but it has worked great so far! Plus, it's freeeeeeeeeeeeeeeee!
After you've downloaded it, (I can't post links, but a quick Google search will work) create a scene with only one source, the webcam. Right click the white window on the left side, under "Scenes" and click "Add Scene." Name it something, then click on it. In the window beneath "Sources," hover over "add" and click "video capture device." Same thing, name it something, then it should pop up a window. Select your webcam from the dropdown list to the right of "Device," and make sure the resolution is correct in the "video" section. You shouldn't need to adjust other settings. If you record out of a mic other than what's in the webcam, make sure the mic you want to use is selected in the dropdown list under "Audio Input Device." From there, click "OK."
Set the overall recording resolution in "settings>video" to 1920x1080p, and the both the max bitrate and buffer size in "settings>encoding" to a number that isn't too much for your PC to handle. For 1080p, I use 3200. Make sure both the max bitrate and buffer size are the same values. If your PC can't handle it, (in which it'll say "High CPU usage! Try lowering your bitrate." down in the bottom left) just tweak the numbers until it works fine. If you need some further help setting it up, there are quite a few tutorials online or I could help you out here on the forums.
Also, you might want to record in .mp4, to do this, go into settings>broadcast settings and replace ".flv" file extension in your "File Path" and "Replay Buffer File Path" to ".mp4". You'll also want to change the path to a location that's easier to find.
Once you want to record some video, just click "Start recording" and you're good to go!
Good luck!
Edit: Since you said you wanted to record for your gaming channel, I'm assuming you want to record your webcam for a facecam. To save time, you can add both your TV screen input and your webcam input at the same time! Just click "Start Preview," (it won't be recording, just previewing) then click "edit scene" and drag one of the corners of the webcam video to make it smaller, then drag the whole video to a corner. From there, add your game screen video source, and put it a layer behind the webcam. Voila!
Fun fact, this program is what tons of Twitch.tv streamers use, and if you want to get SUPER fancy, you can add image overlays, moving text, green screens, and notifications in your scene. I've attached a screenshot what my OBS streaming setup looks like:
