The time period you mention is right about dead-on for the introduction of spreadsheets on microcomputers and personal computers, which is perhaps one of the most (if not the most) revolutionary moments in business computing. Visicalc, released for the Apple II in 1979, is generally discussed as the first computer spreadsheet. This isn't exactly true by some definitions, but Visicalc was significantly more popular than any of its predecessors (e.g. LANPAR which is technically interesting but obscure) --- so popular that it's considered a major driver in the success of the Apple II and late the IBM PC when it became available for that platform.

So, while Visicalc comes in for the second half of the period you mentioned, I think it's a good moment to focus on (we have to be a bit selective, because computer history is such that a lot changes in a 20-year span). Visicalc was most popular on the Apple II, which was expensive but desk-sized and generally fairly recognizable as what we'd call a "desktop computer" today. Visicalc was not "graphical" software, it ran in text-mode - meaning that it made some effort to draw something we'd recognize as a graphical interface, but did it by sending various box and line characters to the screen. In general, the appearance was quite primitive. As a limitation of using text-mode, the display was logically 'small,' in that very few rows fit on the screen at a time. There was no mouse support (mice existed in academic UI work and on some fairly experimental computers at the time, but were not yet familiar to business users), everything was done via textual commands, and a user would be expected to study a fairly hefty manual to learn to use the software. All in all, though, if you saw VisiCalc running on a computer you would probably recognize it as a spreadsheet. It worked on a grid of numbers, and had roughly the same capabilities in doing mathematical operations between the cells - as long as you kept your operations reasonably simple, there was no extended math library like we expect from modern spreadsheets. VisiCalc also didn't feature true forward-solving of your equation dependencies, so instead of updating in "realtime" you would make changes to the spreadsheet and then tell it to recalculate over and over until the numbers "settled".

Here's a little microcosm of computer use at this time: VisiCalc shipped on floppy disk, depending on the kind of computer you were running it on you would probably always run it directly off the floppy disk. The Apple II had no hard disk drive and in the first generation IBM PC it was an add-on feature, so using computers via swapping out multiple floppy disks was the norm at the time. Having a higher-end machine often meant having two different floppy drives to make this easier; the popularity of two drives is somewhat immortalized in Windows today by fixed drive lettering starting at C:, with A: and B: reserved for the typical two floppy drives. So, a typical user would insert the VisiCalc disk and turn their computer on, essentially "booting" directly to VisiCalc. This time period was essentially before operating systems in the modern sense existed - personal computers typically had some kind of BASIC programming environment implemented in their ROM, and then there were more sophisticated environments that could be loaded from disk, but most major applications were intended to run directly on the machine without an intermediary operating system.

You asked about options to use this software today - the PCjs project is a very cool effort to build javascript emulators for early PCs. Their home page emulates an IBM PC, and if you check out the list of disks available (below the 'monitor') they have the PC release of Visicalc! https://www.pcjs.org/
There's also a project called DOSbox that emulates early versions of MS-DOS so you can run the wide range of software built for that proto-operating-system. I'm sure there's a wide range of early Apple emulators too, but I'm less familiar with them. I'm also doing a bit of a disservice by mentioning only the IBM PC platform and Apple platform here, the early days of PCs were much more competitive than that with a variety of interesting hardware and software competitors on the market. But, Apple is still around today, and the IBM PC was the springboard for Microsoft, so they're certainly the most memorable.

VisiCalc is widely considered a seminal moment in computing, so there's a lot of information about it and its milieu online. Here's some articles about it, though, that are particularly notable for having been written by Dan Bricklin himself, one of the creators of VisiCalc. http://www.bricklin.com/history/intro.htm