A single phase transformer consists of two highly inductive coils wound to an iron or a steel core. The winding connected to the AC supply is know as primary winding and the other one is called as secondary winding. The primary and secondary windings are totally isolated from each other as well as from the iron core.
Thus there is absolutely no physical connection between the primary and the secondary winding.
As soon as the primary winding is connected to a single phase AC supply, an AC current starts flowing through it. This current produces and alternating flux in the core. Most of this varying flux gets linked with the secondary winding and then it induces voltage into the secondary winding according to the Faraday´s law of electromagnetic induction.