This is in the realm of TV and FM radio antenna design.
The unit you show is a simple type of dipole antenna made from a length of 300-ohm twin-lead antenna wire, and designed mainly for use for FM radio. Ideally you stretch it out as Pederv says, with the two arms horizontal and the center line running down to plug into the antenna input of the card.You can hook the ends and center to pins or nails or something, or fasten it to a long stick and mount the stick somehow. It is directional - it picks up best PERPENDICULAR to the long 2-arm direction - that is, it is worst ALONG the stretched out arms.
This antenna is sized for radio waves in the FM radio band, which is just above the frequency range for the old VHF-Low (channels 2 through 6) analog TV band. So it will pick up those low-channel stations not too bad, but it will be poorer for the VHF-Hi band (channels 7 through 13) and probably much worse for the old UHF range (channels 14 through 69).
Now, that antenna will work fine for local FM radio. The dilemma you have for TV, though, is that all TV in the USA switched to digital, and MOST of them also switched to the UHF frequency band as they did that. SO, this antenna is likely to be very poor for local OTA TV unless your preferred station happens to be in the channel 2 through 6 range. "Pixelated and jerky" is what you get with weak digital TV signals. Analog weak signals looked like a bad picture with "snow" and odd colors. Digital weak signal just makes the receiver freeze on the last good signal it gets until it gets a good one again.
If you want reasonable reception from OTA transmitters in your area, check the channels they are on for starters. I expect some or most will by above channel 14. For those you can buy many different small antennas designed for indoor use. They are small because the wavelengths are short. They are widely available in electronics shops, TV sales shops, big-box stores, etc. The problem is not finding some. It is deciphering which ones are any good, because they ALL are the best in the world! If you can, search the web a bit for actual performance test-based reviews of antennas to help identify the best in your price range. More expensive and complex, and usually larger, will usually get you a better signal, but you won't want the biggest and best for average home use. If you really want to go techie and "roll your own", look on the web for Gray-Hoverman antenna design developments.
Don't forget, IF you have cable TV service in your place, there are lots of channels there. Many will be digital signals. Some of those will be HD, some will be only old standard-TV quality. Depending on your local service, there may be still several analog TV channels on your cable. I'm sure your card could tune in those if you want to.
Check your card's manual carefully. There are various designs around. Some, for example, have two tuners inside and two antenna input connectors. But the way they work is that one connector is associated with only one tuner capable of handling FM radio and OTA digital TV done by the ATSC coding system, while the other connector / tuner set handles only digital TV with Clear QAM encoding on cable systems. Some are arranged differently with all tuners able to handle all tasks. So read your manual and make sure you connect whatever antenna / signal source you have to the correct input.
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