I was hoping to perhaps get some advice about a project idea. There is a device in my home that transmits data readings via a short range radio at 433.82 Mhz. Would anybody know how/if I could pick up these reading with am arduino or galileo board and display them on a simple screen?
There is a range of digital radio transmitters/receivers working at around 433MHz which can be controlled by an Arduino. However, you'd need a lot more information about the signal you're trying to decode to know whether these were suitable to handle it.
If your device is a remote temperature sensor or type of environmental monitor, much work has been done to receive, decode and display the data. Google "arduino decode weather station protocol" for many ideas.