I would like to buy a Helios 44-2 lens, but I need to know if my Nikon D3300 will allow me to take pictures with it since the lens has no pins.
Will there be any other problems?
Actually, quite a few problems. Just my personal opinion, but you'd be better off saving pennies and getting an APS-C 50/1.8G or 35/1.8. The only reason to go to the vintage glass is if you like being a stubborn cuss, with a fascination for vintage glass, who does stuff just to prove you can. Who also knows how to accurately grade a vintage lens both in condition (fungus!) and function, and knows a cheap, good, reliable CLA guy.
The cost of a vintage lens is not the only cost of a vintage lens. You need to factor in the adapter, probably a CLA (look. On eBay, "mint in the box" can mean "saw a lens in the box" and nothing more).
You will not have autofocus. You must set the aperture on the lens's ring, not from the camera. You will not have accurate metering (until you upgrade to a D7000 body or above). You will not have lens EXIF information like the lens name, focal length, and aperture setting used. You will not have film-era viewfinder aids to help you focus. You can't use all the modes on your camera dial, because the camera can't control the lens's aperture setting.
And because you're adapting M42 to Nikon, you will not have focus to infinity, unless you use an adapter with a glass element in it to act like a short teleconverter. Bad part is, it's gonna act like a short teleconverter, adding softness, reducing max. aperture, and increasing focal length. If you remove the glass element, you won't be able to focus past 10 feet (maybe less). As the Helios 44-2 isn't a macro lens, this may not be ideal. Hence my initial recommendation.
If you're bound and determined to use a vintage manual lens, then I'd say, pony up a bit more dough and go for a Nikon pre-AI 50, 55, or 58mm F-mount lens. On a D3x00 body, the lever damage you'd get on a higher-end body with a pre-AI lens won't be an issue, you won't need an adapter, and it'll be a great quality lens. If you can spend more, consider finding an Olympus OM-mount 50mm f/1.8, and throwing on a Leitax mount replacement. Another very nice, very cheap, lens but an expensive adapter--without a glass element.
Nikon F, unfortunately, is THE most problematic dSLR mount for adapting manual lenses.
Don't worry about the pins, as long as you can handle manual exposure, aperture and focus. You will need to shoot in manual mode and tell the camera to expose when it thinks there is no lens attached. Most likely though you will not be able to achieve infinity focus, because of the flange-focal-distance. Here is a follow-up-read (or 'duplicate'): How will old M42 lenses work on a Nikon camera? and here: How can I use a vintage M42 manual prime on an entry Nikon DSLR?