To get started you first need to purchase an SDR radio device, this plugs into a USB port on your PC (or Mac or whatever). You can buy the cheaper units here...
Buy RTL-SDR Dongles (RTL2832U) .. you are looking for the 'RTL-SDR Blog V3' for around $23, they are actually very good value and perform very well.
When you get that, you must plug it in and install the drivers for it... Check
www.rtl-sdr.com and search there for those. Connect some sort of antenna to it via it's SMA connector. Download the free SDR Sharp (SDR#) software from
www.airspy.com. Fire up SDR#, tell it you are using an 'RTL-SDR' at the very top left and hit play. With a mediocre antenna connected, to do a basic test, you should easily pick up broadcast FM radio stations between 88 and 108 MHz as displayed on top. Make sure the software is set to 'WFM' mode, click on the frequency readout on top to tune up and down. For aircraft, tune from 118 to 137 MHz in 'AM' mode. From there, if you get the bug, you can purchase more expensive/better SDR devices and the world is your oyster regarding antennas and what you can receive. I hope this helps.
Terry