Human computers did execute "programs".
The programs were written (typed up) instructions that included a sequence of steps, such as what numbers to take off which line on a worksheet, what operations to perform, where to put results back on a worksheet, what to do next (including "loops", e.g. repeat n time, or for the number of items in a column on the worksheet.)
The "programs" were written up by the scientists (essentially programmers). The room full of (most often) women would be trained to follow these instructions, and their work was sometimes duplicated by another "computer" for error-checking/fault-tolerance.
Why do I know? My mother claims to have done this as a grad student at U.C. Berkeley during WWII. Also, see the book "When Computers were Human", by D. Grier.
All done on paper, and later after the industrial revolution, on mechanical calculators.