Radio in the USA had its big growth from the mid-1920s to the end of the 1930s. First note that commercial radio broadcasting in the USA began in 1920: the first station, KDKA in Pittsburgh, starting broadcasting then. KDKA was owned by Westinghouse, and their broadcast antenna was on the roof of the Westinghouse Electric factory in Pittsburgh. Westinghouse made, among many other things, radio receivers, and giving people something to listen to was a way to help sales. By 1921, there were 5 licensed commercial radio stations. In 1924, the number of stations exceeded 500.
Early radio receivers were expensive: in 1916, the cheapest radios were about US$35, and more expensive ones were often $100-200. Improvements in radio technology made radios better and cheaper at the same time. When those improvements were joined by the use of plastics such as bakelite (reducing the labour costs of making the outer bodies of radios, by replacing wood), radio prices fell as low as $10 (big-brand radios might still cost about $35, but those were much improved over the $35 radios of 1916). Simpler radio technologies, such as crystal sets, were available for $1 to $2 (but only suitable for personal listening, due to the lack of amplification).
How affordable were these prices? Hourly wages were often about 30-60 cents per hour, and weekly earnings about $15-30. Thus, cheap radios cost about a week's wages. Radio prices were comparable to many other home appliances - an electric toaster might cost about $10, a gas stove/range about $70. For a comparison with some foods, bread cost about 20 cents/kg, and steak about $1/kg. The immediate burden on the buyer was eased by being able to buy on credit - about 70% of radio sales in the late '20s were "buy now, pay later" Some people were unable to afford radios, but the middle classes could afford them.
Advancing electrification, especially in rural areas, offered even more people the opportunity to listen to radio (in 1935, only 10% of US farms were supplied with electricity, so it made a significant difference).
While the Great Depression left some families impoverished, and unable to afford a radio, radios were still affordable for most people. Once a radio had been purchased, it provided free entertainment, and was attractive as a potential money-saver compared to other entertainment choices (of course, repairs might need to be paid for). The 1930s hit cinemas hard, with about 1/3 of the cinemas in the US closing. Radio would have been one of the factors contributing to this, and radio also benefited from it - if cinemas closed, families were more motivated to buy a radio.
In 1925, about 19% of US households owned a radio (at least one radio; some owned more than one). By 1930, about 12 million US households (about 40%) owned a radio. By the end of the decade, the number of radio-owning households exceeded 28 million (83%). After that, with a large majority of households owning radios, there wasn't much room left for more growth. As new things like television came along, people still owned radios, and would still listen to them. However, the typical radio-owning family in the 1930s listened to it for over 4 hours a day, often together, and television would come to replace the radio in this role.
(But I'll leave the growth of television and its impact on radio to future questions and other people.)