The assassination of the Archduke didn't actually produce all that much of an uproar among average people in Austria itself, but it severely pissed off the Imperial government. Violence against Serbs flared up throughout the Balkans, especially in Croatia and Bosnia (and even more especially in Sarajevo where the assassination occurred) where ethnic tensions were already very high and waiting for something to set things off. The A-H government didn't do anything to stop any of that and in fact encouraged the whole shitshow. Local officials in the territory of Bosnia-Herzegovina did at least attempt to restore order, but they weren't especially successful. Later a militia group called the Schutzkorps was organized that carried out persecutions of Serbs on a more organized basis, but they don't really do anything interesting until the interwar period. Serbia and Russia were not happy about any of this, but the A-H government was out for blood over the death of Archduke Ferdinand, and perhaps more importantly saw the whole thing as a pretext to invade Serbia, which had gained a lot of territory in the 2nd Balkan war and was seen as a lightning rod for Balkan pan-Slavism and therefore a threat to A-H's control over Bosnia-Herzegovina. The assassination happened June 28, and by July 23 A-H had sent an ultimatum to Serbia. The ultimatum required them to work to annihilate pan-Slavic and Serbian nationalist organizations, suppress anti-AH propaganda, and allow AH to conduct its own investigation into the archduke's death. AH didn't expect Serbia to comply, and they and their allies in Germany were already mobilizing when the ultimatum was issued. They had 48 hours to comply, and knowing full well AH would probably invade anyway the Serbian government didn't waste their time with it and just went straight to Russia to appeal for aid and mobilized their own army. Russia accepts, and when AH declared war on July 28 with Germany's blessing, they begin total mobilization. By August 6th, France, Britain, Germany, Russia, AH, Serbia, and the Ottoman Empire were officially at war and offensive operations had begun.
The Austro-Hungarian army in 1914 was split into two main groups: the first smaller group consisting (initially) of about 270,000 men under the 5th and 6th armies invaded Serbia, while the much larger group of about 1 million men divided into the 1st, 2nd, 3rd, and 4th armies was deployed against the Russians. The Imperial military effort on both fronts can be described generously as hideously incompetent. In Serbia the army, then under the command of general Oskar Potiorek from Slovenia, shelled Belgrade and the surrounding countryside from the 28th of July to the middle of August, while the army set up pontoon bridges to allow safe crossing of the Drina river marking their shared border. The first major battle occurred on August 15th when Serbian forces dug in at Cer mountain repelled AH's main thrust toward Belgrade. The battle was extremely costly to both sides but was still a resounding strategic defeat for the Empire, but AH could much better stand to lose men than Serbia, and they just launched another offensive farther north. The Serbians fought a losing battle to hold off the Imperial army, and even launched a few ill-advised attacks across the Drina into Bosnia, but again despite punching above their weight they just didn't have the manpower or supplies to really stand a chance. The controversial decision was made in early November to withdraw, abandoning Belgrade to AH but giving the Serbian army a chance to rest and resupply itself. AH advanced very quickly after that and occupied Belgrade after a few days of fighting against partisans, but left themselves overextended and with a fairly porous front. The entirety of the now rested and reinforced Serbian army counterattacked, and were able to encircle parts of the Imperial army and inflict severe damage on others in attacks on their exposed flanks. Potiorek ordered a full withdrawal back across the Drina into Bosnia on December 5th. All told, casualties amounted to ~170,000 on the Serbian side and ~215,000 by AH. Potiorek was sacked December 8th and replaced by Archduke Eugen of Austria. Fighting wouldn't start again until the Fall of 1915.
Things went even worse on the Russian Front, at least for Austria-Hungary. The Russian army attacked first there, rapidly pushing the Imperial army back in Galicia, now in Western Ukraine. They had some initial success, dealing
serious defeats to the Russians early on, but Austro-Hungarian incompetence and lack of strategic coordination hit just as hard here as in Serbia, and an
attack by the already dangerously overextended third army resulted in a complete rout and a collapse of the eastern flank.
An attempt was made to assist the battered 3rd army, but the forces committed there weren't enough to halt the Russian advance there and provided an opening for a counterattack by the Russian forces which had previously been in retreat on the northern side. The whole front was in complete retreat by the end of August, and despite the redirection of troops from the Serbian front the Russians had almost complete control of the region by the end of 1914 and had begun laying siege to the fortress at
Przemyśl.