The first thing you want to do is to check that the pins on the foot of the flash match the contacts on the hotshoe of your camera. They need to match in both the number of pins and placement so that the pins will touch the contacts exactly. Most sellers will show a picture of the foot of the flash. See also:

• Is flash brand X compatible with camera brand Y?
• Are Yongnuo flashes interchangeable between dslr's or are they brand specific?

Secondly, you'll want to read through the specs of the flash to see how compatible it might be. If the flash is not OEM (original equipment manufacturer; that is the same brand as your camera), it may be compatible with most, but not all of the features an OEM flash can perform, and you'll want to see what might be missing from the list. The main features you're probably looking for are TTL (Through-The-Lens metering based power automation) and HSS (high-speed sync AKA FP or focal plane sync, which lets you use a shutter speed faster than your camera body's sync speed, if your camera body can perform HSS; the D3x00 and D5x00 Nikon bodies cannot.)

See also: What features should one look for when selecting a flash?

Thirdly, you'll probably want to google to see if there are issues with your specific model combination, particularly if either the flash or the camera body is brand new with new flash features. Sometimes the camera company makes changes to the hotshoe/flash communication protocol and while the OEM flashes will still work, 3rd-party flashes which were reverse-engineered off older camera bodies may have issues. Getting a 3rd-party flash with firmware upgrade capability might help with these types of issues. Be aware, however, that it's unlikely someone may have the exact same combination of gear, and that you may just have to buy and try to see; so choosing a retailer with a good return policy may be the only thing you can do.

Last, but not least, in the case of Neewer, understand that Neewer doesn't actually make any flashes. They rebrand flashes from a number of other Chinese brands, such as Yongnuo, Godox, Jinbei, Triopo, and Meike. If you're doing research, it's sometimes simpler to do so with the "base" brand model, rather than the Neewer one, if you can discover what it is.