Recording technology was still in its early days in the 1950s, singers usually performed live with their musicians, which was often done in a single large room. Only a few microphones were used, and they were often mixed down directly to mono or stereo tape as multitrack recording was not yet common, although it already existed.
The “gramophone”, which later evolved into the turntable, had already been developed in the United States by Emile Berliner in 1889. In 1901, 10-inch disc records were introduced, followed by 12-inch records in 1903. 78 rpm discs became standard in 1925, followed by the modern 33.3 rpm 12” LPs in 1948 and the 45 rpm 7” single in 1949. Most songs were released as mono tracks in the 1950s – the first stereo vinyl LP was released in 1957, and it took a few more years until the new stereo format actually became popular in the 1960s.
While all of this sounds quite primitive, the sound of those recordings has often been quite good, which is partly due to the fact that some of today’s best microphones already existed back at that time. After Georg Neumann’s factory in Berlin had been bombed in 1943, he was able to introduce the U47, U48, M49, and M50 condenser microphones only a few years later. While American RCA ribbon microphones were still very popular in the 1950s (used for most Elvis Presley recordings for example), pop recordings in that decade were mostly done using the new condenser microphones. Some of the original Neumann microphones still have a cult following today, as they can be used to recreate an original vintage sound, while newer Neumann mics such as the M149 (introduced in 1995) can be found in most project and professional recording studios nowadays.
It should also be noted that the Fairchild 670 stereo compressor was developed and used in the 1950s, which is still considered to be one of the best compressors of all time, and which was often used as a stereo bus / mastering compressor. The Fairchild 670 was used on many of the recordings of the 1950s, 60s and 70s, and it’s been credited for being at least partly responsible for the “warm” sound of those decades, until it got slowly replaced by more modern solutions such as SSL’s stereo bus compressor in the late 70s and in the 1980s. The 670 is regaining popularity nowadays, and several companies are now building (quite expensive) clones of it again. And yes, there also are 670 software plug-ins that are quite good.