Ah, the Pokeball. It is a ubiquitous item for any trainer, new or old, on their path to becoming a Pokemon master. The pokeball allows its user complete captivity over the Pokemon they capture it with, although control is dictated (in most cases) by the amount and level of badges the trainer possesses.
As we know and understand them in this modern era, pokeballs are mass-distributed items, purchasable in any shop in any region. They were originally crafted from Apricorns by hollowing the apricorn out and fitting it with a capture device so as to contain the pokemon. Since then, though, they have been mass manufactured by Silph Co. and Devon Co., made available easily in most every retailer.
But what about the time before pokeballs? What about the world as it existed before there was a widespread ability to capture and tame these wild beasts? Can you imagine living in a world where you are under constant threat of attack from nigh-unstoppable beings?
In a world where gargantuan beasts can unleash bursts of concentrated energy from their mouths, humanity really fares poorly. Comparatively, we are severly under-equipped to deal with this level of raw power.
Pre-pokeball humans must have lived in reverent fear of Pokemon, and must have treated them as deities. That would go a long way to explaining why there were carvings on temple walls of Mew. Mew, the smallest and most visually accessible of the Pokemon, would have been considered akin to a true god to primitive humans. The amount of power in such a small frame would stagger early humans.
In the Pokemon canon, particularly the anime, Ash and friends come across the ruins of Pokemopolis, and with those ruins are ancient artifacts were found that contained giant versions of pokemon. There was a giant Alakazam, a giant Gengar, and a giant Jigglypuff, all contained within the unearthly urn, the dark device, and an ancient paintbrush respectively.
This goes to show that there existed ancient ways of capturing pokemon, though how these items work is never truly explained. An assumption can be made that they are somehow magical; this defies an actual explanation, but it is the only thing that can be offered instead of a quantifiable explanation.
Aside from this, other methods of capturing or controlling pokemon from ages preceding the anime/games are shown, all of which to be inherently magical. The major thing to take away from that, though, is that there are very few of these items, each one being unique. This means that up until apricorns started being used to make pokeballs, humans existed in a state of fear.
Of course, it is possible that humans created lasting bonds with certain pokemon; Ash's Pikachu is virtually never in his pokeball, and exhibits the ability to leave it on his own, without Ash calling for him (same with James' Victreebell).
So for those who weren't able to make a bond with a pokemon, it would have been a very scary world to live in. Thankfully, Silph Co. was able to create a way to reliably capture these Pokemon.