I started DXing by accident. My father taught me how to buy stock. Usually single shares for birthday and Christmas, but shares. By age 11 or 12 I had a share or two of Storer Broadcasting, and thought it was important to listen to as many Storer stations as I could. I found local WJW, of course. And then I could hear WWVA in Wheeling and WSPD in Toledo. The others were harder, but I soon realized I could hear all kinds of fun stuff on AM at night. It became a game, a challenge, and something my friends at school didn't all do.
I joined a radio club, and was an official DXer. There was no minimum age.
In the later 50's and early 60's (I moved to Ecuador in '63) nearly every frequency was empty or close to empty on Monday morning; that was when stations did transmitter and studio maintenance. Equipment in that era was in need of constant maintenance, since most of it was still vacuum tube based and overall reliability was far less than today's gear.
I was in Cleveland, Ohio. So at midnight on Sunday, stations in the Eastern time zone signed off... almost all of them. That uncovered Central zone stations in the last hour of Sunday broadcasts. An hour later, it was Mountain, and then Pacific zone. Then there was at least an hour or two before EST stations came back on.
I had bellwether stations like 1370 in Montana and 920 in Albuquerque that told me if the rest of the night would be good. If 920 was being chopped up by the co-channel in El Paso, I looked for the last hour of many Mexican stations. And then on to the West Coast where ones like Riverside, CA, 1kw on 1440 would be an indicator if it was not overwhelmed by the co-channel in Medford, OR.
In the meantime, many stations did on-air frequency checks. They'd run tone and a distant monitor would do the legal verification of being on frequency. The radio clubs had many-page lists of the frequency checks, which were scheduled. Other stations did DX tests just for DXers, sometimes more than a dozen or two on one morning.
There were also random tests, where an engineer doing maintenance would put their station on the air for a bit to check something out. As the FCC was stricter then, they nearly always gave an ID as required.
After 3 AM Europe might become viable, with occasional Middle Eastern and Northern African stations. And the sign-ons from Argentina, Brazil and Uruguay were frequent catches. And, of course, after 3 AM the chances for Hawaii, Australia and New Zealand were good. I heard Honolulu stations in 650, 690, 760, 870, 1040, 1270, and 250 watt KIKI on 830 among others I forget now.
I heard Alaska once, Fairbanks on 660. And then there were oddities like the 50 watt AFRTS station on 780 at Ramey AFB, Puerto Rico. Some of the Caribbean Island stations from places you had to look up on a map came in at their AST early sign ons.
Finally, as 6 AM EST sign-ons came around, the absence of CST "big stations" often allowed smaller facilities in the EST zone to be logged as they signed on. And many EST daytimers had a Pre-Sunrise Authorization and could sign on at 5 AM, so there were many catches to be found, with each Monday morning being different due to conditions.
In the nearly 5 years that I did AM DXing from Cleveland, I got written verifications from over 2,500 stations and perhaps 300 more that did not verify. All 50 states, all 10 Canadian Provinces. About 70 countries.
What was the most fun was the fact that there was very little networked programming back then, particularly at night and in overnights. So every station was different. They were all fun to discover, unlike the automated music or syndicated network talk shows on so many stations.
Of course, a by-product of DXing was visiting stations. Any trip meant my mother waited in the car in the parking lot while I toured yet another radio station. Station visits in my home town resulted in a part time job at WJMO & WCUY, located near where I lived. And that started my 60 year career in radio...