I had a box of Remington 9mm 115 gr +P hollowpoints I bought in 1991. Half the box (32 rounds) were loaded into two Glock 17 magazines, the rest stayed in the box.
Fast forward 19 years to 2010. I shoot all 32 rounds from the two G17 mags, without any hiccup. These mags had been unloaded and reloaded with the same cartridges, about once a year... but other than that, no maintenance. The 18 remaining cartridges in the box also get shot without any hiccup.
I have also shot 20 gage and 12 gage shot shells that were more than 30 years old. Again no problem.
My father-in-law had some 1951 vintage 45 ACP that we shot in 1995 (44 years old). No problems, but it seemed to smoke more than modern ammo... maybe it was the mil-spec powder of the era, or maybe it was the age. But the ammo went bang.
No special precautions were taken to store this ammo. It was stored indoors and it never got wet. I don't think you need to do anything else. Store it the way you would a book, or a screwdriver, an electric drill, or a pair of socks.