As in many other achievements, the creators of the first space station stood on the shoulders of giants. This phrase usually means that there was important preliminary work made in relevant areas. That preliminary work significantly helped in creation of Salyut-1 - or DOS, as it was called internally, this acronym means "long-term (dolgovremennaya) orbital station". DOS was made by the same organization which launched Sputnik and Gagarin, the name at the time was TsKBEM, now it's known as Energiya. In addition to their own solutions, they used the work made by the organization, which created the rocket Proton - TsKBM, now more known as NPO Mash. The confusing names remind about the Soviet secrecy...
TsKBM worked on the program of military orbital station called Almaz ("diamond" in Russian) since 1960s, as a response to the American military station program MOL (Manned Orbital Laboratory). By the end of 1960s TsKBM had the body of the station made to be launched on Proton rocket. However, internal systems - the important parts, which actually allow the station to be habitable - weren't ready. The specialists in TsKBEM, striving to have a successful manned program soon after losing the Moon landing, had good life support systems designed and tested for Soyuz spacecraft at the time, but were lacking the station shell. TsKBEM was successful in convincing the authorities that they can make the space station fast, if they were given that Almaz body and the necessary Proton rocket to launch it.
Another critical component of the space station - the docking port - was also already built for Soyuz spacecraft. A version of it was designed for the Moon program, and tested in orbital Soyuz flights - automatic and manned. So, the whole DOS could be roughly split into these parts - shell, life support systems and other systems designed for Soyuz, with modified docking port. The systems taken from Soyuz included solar panels - energy source for the station - and radiators - necessary for maintaining the proper thermal environment onboard.
The plans inside multiple Soviet design bureaus led to some parallel development, so as a result USSR had "military" stations and "civil" stations, which all were launched by Proton rockets over the next decade. Building and testing multiple stations allowed for some learning and improvements in subsequent models.