From the point-of-view of someone at the time, you interacted with early computers in the usual way.
From the 1930's onwards, business and some science used IBM and Remmington-Rand mechanical punched-card processing machines. You set up the specialized gear-based machines for your job (payroll, overdue accounts, super-hard math equation), punched data onto cards, fed them in, and the output was either printed (all caps), or punched onto more cards (for example, payroll checks). Some systems used a long paper tape (which had been used for telegraphs for 50+ years) or very early (1900) systems had numeric dials -- you hand-copied the answer after it finished. But however you did it, it was 1 run with 1 set of results.
A 1950's computer (UNIVAC, IBM702, Honeywell D-1000) essentially replaced the middle part of that system. If you worked at Prudential, you typed the same cards, fed into the same readers, and generated the same printed reports. That was on purpose. Businesses could buy a computer without having to retrain the entire data-processing staff.
It wasn't that simple. Quickly we started using new magnetic tape for I/O. And computers weren't seen only as "like the old machines, but faster" -- early on we knew they could also do more. There was some early work interacting using light pens (SAGE). But in general, we thought it was normal to have Batch Jobs, which were "1 run, 1 result, no interaction" for quite a while.
An early 1960's manual gives a nice feeling for how computers fit right into the old system: Chapter 1 explains how ADP (automatic data processing) consists of EAM and EDP. The old mechanical systems are Electric Accounting Machines, while computers are Electronic Data Processing machines. Using either of them is the same job. Ch2, page 11+, gives a nice history, then page 31 starts on EDP (again, computers). It explains how the major difference is only programming (which someone else does) and knowing how to mount tape reels sometimes.