This is something few people think about in WWI... the fact that you had a whole army riddled with all sorts of nationalities and languages that somebody had to coordinate.

First, we have to make a distinction between command language and regimental language.

Command language was simply the army's language for orders, documents and everything else written down in some official form. Officers were required to speak fluent German by the time they finished officer school, as well as French (of course the international language of the time) and two other languages of the Austro-Hungarian Empire. All regular soldiers were drilled to know the 100 or so basic commands in German so they could be commanded by any k.u.k. officer if necessary.
Command language of the proper k.u.k. Army was German, although in Galicia Polish was quietly tolerated for local commands. But also, in the Ausgleich of 1867 the Hungarians had demanded and gotten their own armed forces. Officially a militia but practically a full and partially even better equipped army in itself the k.u. Honvéd in Hungary and Domobranzen in Croatia had Hungarian and Croatian respectively as their command languages. And lastly, as a result of the Hungarians getting their own militia/army, the Austrians had to have one as well, the k.k. Landwehr, which, again, used German.

Regimental language is far more interesting and complex. Obviously a regiment's language composition depended mostly on where it was stationed and as such from which area it drew its recruits. Regimental languages were officially recognised languages spoken by a certain percent of the regiment's troops. As such we can find anything from purely German regiments like the Infanterie-Regiment „Hoch- und Deutschmeister“ Nr. 4, stationed in Vienna, with a nationality of 95% Germans and 5% other to such diverse regiments as the k.u.k. Ungarisches Infanterie Regiment "Erzherzog Peter Ferdinand" Nr. 66, stationed in Uzhhorod on today's Ukraine-Hungary-Slovakia border, with 25% Magyars, 46% Slovaks, 22% Ruthenians and 7% other. There is a whole list for all the k.u.k. regiments on the German Wikipedia.

Now, all of the regiment's commissioned officers (lieutenants up to captains) were also required to speak all the languages of their regiment. For this, they were given three years after which they had to face a commission and demonstrate that they were fluent enough for service. If an officer failed, he was provided with an additional two years and if he failed again he was barred from further promotions.
Of course, as with everything the k.u.k. Army did, the implementation had its issues. Mainly that many officers couldn't be bothered to learn their slavic languages properly and created something generally referred to as "Armeeslawisch" (army Slavic), a jumble of various Slavic languages mixed with German words in the typical "that'll do" attitude.

On the other hand, around 75% of officers in each branch considered themselves ethnic Germans in an army where only a quarter of the regular soldiers did (the great three being 25.2% Germans, 23.5% Magyars and 16.5% Czech). And still about every second one spoke Czech, every third one Hungarian and every fifth officer Polish. Italian was also still somewhat large as a second language in the army, although it had lost most of its use after the loss of Austrian Lombardy-Venetia in the Wars of Italian Independence.

Another thing of the Anschluß was that the military laws had to be renewed every ten years starting in 1868, which left many minorities with hopes of getting better conditions for themselves. Especially the Hungarians had very active lobbying to allow Hungarian regiments in the k.u.k. Army to use their own language as command language, but influential Czech and Polish politicians were major players in the game as well. Normal soldiers would join in as well, officers would regularly encounter instances where soldiers would not respond to the roll call with the proper German "Hier!" but in their own language. This never led anywhere though as both the War Ministry and the Emperor were very much opposed to such a profound change.

But this is mostly pre-war stuff... in regards to your specific question of how the army managed language problems during WWI the answer is probably "poorly". Due to catastrophic early offensives of the Austro-Hungarian Army quite a lot of officers were taken out of service dead or as POWs, which meant that their positions had to be filled with reserve officers. Reserve officers who had no connection to their men, had not enjoyed 5 years of time to learn their regimental languages and quite possibly not even finished any proper officer schools.

Sources:
Kronenbitter, Günther: „Krieg im Frieden“. Die Führung der k.u.k. Armee und die Großmachtpolitik Österreich-Ungarns 1906–1914

There was a really excellent answer posted to this awhile back. My search skills are failing me. I'll try to link to it when I'm not on mobile.

The jist, from what I remember, was that battalions would pick whichever language was most common among them. Sometimes that language wasn't anyone's mother tongue, but it was still shared among the most men. Those who didn't speak that language had their comrades translate for them.