Almost anybody can grab a USB TV tuner card and start monitoring the airwaves. To be able to do radio transmissions legally you’ll need your amateur radio license and suitable equipment. There is wide variety of equipment you can buy and build. On new interesting new radio kit is HamShield I saw mentoned at HamShield Puts Your Arduino On The Radio article. HamShield is an Arduino shield that lets your Arduino talk to far away people and things using VHF and UHF amateur radio bands (Coverage: 136-170MHz, 200-260MHz, 400-520MHz). This shield has built-in 250 mW amplifier. The HamShield supports both voice and packet radio modes. The HamShield is powered by the Auctus 1846S radio transceiver IC (chip used on for example walkie-talkie radios). You can find HAMShield Specifications agt GitHub. The project’s sandbox already includes things like setting up mesh networks, communicating over APRS, setting up repeaters or beacons, monitoring weather stations, and a whole host of other ham radio applications.
The developers are raising money now at Kickstarter.