That looks like a BGA surface mount component. It is possible to solder these parts to a PCB by hand using a variety of different methods.
- Use a hot-air rework station
- Use a reflow oven. This can be a professional one, or more commmon for hobbyists is to build your own from a toaster oven or a hot plate. For really cheap you can try using the toaster oven/hot plate without any extra controlling circuitry, just carefully watch the process.
Note: If you use the second option, be sure NOT to use the same toaster oven/hot plate for cooking food you're planning on eating or feeding to someone else.
Whichever method you choose you'll want to get a pair of very fine point tweezers, or even better a vacuum pickup tool.
You'll also want some kind of magnifying system. This allows you to precisely align components. Some people use a headband magnifier, others use a full-on desk microscope.
Soldering BGA packages also usually requires solder paste and flux.
You can get breakout prototyping boards for BGA packages, these are a basic PCB board which route the BGA's pinout to some through-hole pins you can solder headers or wires to.