A typical rural branch line of the "good old days" kind, beloved of railway modellers, (eg Princetown or Buckfastleigh) would run on the "one engine in steam" principle for most of its local passenger services. These would be trains limited to run to and from the end of the line and the junction. The engine shed would often be at the line's terminus.
If the branch line was an "extension" of the main line (as in the Paignton-Kingswear branch) and/or had a branch of its own (eg the Brixham branch from the Kingswear line) then the shed would be at the "junction" (Paignton in this example), with limited facilities at the far end - largely due to shortage of space at the terminus.
There would be frequent "visiting" locomotives that hauled the goods trains and "through" trains on most country branches, especially on seaside ones. Through trains were the ones that ran from a major main line terminus through to the branch line terminus. For example you would frequently have long trains pulled by large engines taking trains from London termini to seaside branch termini, such as London Waterloo to Swanage.
Around the later part of the GWR period and most of the Beeching period many branch lines were DMU operated but often these came too late to save the line. In the Thames Valley the surviving Windsor, Marlow and Henley on Thames branches are now operated entirely by captive "one engine in steam" DMUs.
As an example of a less-than-sleepy branch line: Prior to dieselisation the Slough - Windsor branch was double tracked and would often have several engines in steam during weekdays, some serving the "captive" branch train, some on long-haul services and some on goods and coal traffic. The engine shed responsible for the branch locos was at Slough (site now a block of flats).