How the answer is framed depends on what time scale you're asking for. In a broad sense, it paved the way for almost everything we consider essential for modern firearms. In the near term, military doctrine largely remained the same as before on paper, with the big distinction being that it was adapted to account for the longer effective ranges of smokeless powder cartridges.
On a broad historical scale, smokeless powder was so significant because it finally made everything from small-bore (8mm and under) cartridges to long periods of continuous fire to autoloading mechanisms viable. The driving force here is fouling; black powder produces a lot of fouling with every shot, and that meant even with black-powder cartridge rifles (which were generally modern in every sense save the propellant used), you had an alarmingly short effective number of shots before the user had to stop and clean out the bore. Generally, the smaller the bore, the faster the fouling became an issue, so we tend to see black-powder cartridge rifles have fairly large bores (generally on the order of 10-11mm or .40 to .45 caliber). Smokeless powder massively reduces fouling, often to the point that with modern ammunition many rifles can be fired effectively indefinitely without cleaning. In doing so, it made the reduction of bore size viable. This was significant because these large-bore rifles that preceded smokeless powder tended to have comparatively low muzzle velocities. Using .45-70 - the US Army's caliber for their Trapdoor Springfield service rifle - as a baseline, we're talking about a 500 grain bullet going around 1200-1300 fps leaving the barrel. Compare that to the first smokeless cartridges to come along like 8mm Lebel (~200 grain at ~2400 fps) or .303 British (180 grain at 2500 fps or 150 grain at ~2800). The impact here is that the new cartridges have significantly flatter trajectories and generally much longer effective ranges.
The lack of fouling and different pressure curve compared to black powder also made smokeless powder ideal for autoloading firearms, particularly machineguns. While Maxim's patents do predate smokeless powder, the guns he became famous for exclusively used smokeless cartridges, and descendants of his designs like the Vickers Gun showed that a smokeless-powder cartridge allows for indefinitely long periods of firing. Later gas-operated systems to come about would make use of smokeless powder's higher instantaneous pressure (vs black powder's more consistent but lower pressure) to bring about autoloading firearms as we know them today.
Despite the broad historical significance of smokeless powder, however, the immediate reaction at the time by militaries around the world seems to have recognized things like the longer effective range, longer periods between cleaning, and flatter trajectories, but they still held on to a lot of ideas that we'd think of as antiquated today. The 1886 Lebel - the first smokeless-powder repeating rifle - and its contemporaries were very long "full-sized" rifles. The Lebel was over 51 inches long with a 31 inch barrel, the idea at the time still being that an infantryman needed a rifle long enough to reach past one or two lines of men in front of him so there was no danger of friendly fire. Bayonets also remained almost absurdly long often right through WW1 - the Lebel's bayonet featured a 20-inch blade, and the Type 30 bayonet that was common on every Japanese rifle to the end of WW2 featured a 16-inch blade. The idea here was to keep the rifle tantamount to a spear for the purposes of fending off cavalry.
Magazines did end up being incorporated into every service rifle, but not for use as we'd expect nowadays - standard doctrine for nearly all armies was to keep the magazine in reserve until an emergency, with soldiers single-loading over a full magazine until told to do otherwise by officers. Many rifles (the Lee Enfield and Springfield 1903 come to mind) even featured magazine cutoffs to ensure soldiers wouldn't be "wasting" ammunition until officers deemed it necessary. Here it seems a bit counterintuitive until we look from a strategic perspective. Armies at the time were seriously constrained by logistics, and as was the case with many realities of modern war, the impact railroads would have on supply of armies wasn't really all that apparent at the time, so the danger of running out of ammunition while on campaign was very real in the minds of planners.
If you want a good look at what the original plan was with smokeless powder rifles between 1886 and the First World War, I'd recommend taking a look at the engagements in the Second Boer War. It featured a fair amount of "legacy" tactics and strategic situations (poor supply situation and expansive theater) without the jarring immediacy of modern technology forcing practicality onto the warring parties from the outset.