The gas in your party balloons is a genuine Earth product that is an important industrial gas. Helium is generated throughout the Earth's rocky mantle but especially in the continental crust.
How Helium Forms
Helium is manufactured by the alpha-decay of uranium and thorium. An alpha particle, two protons and two neutrons, constitutes the nucleus of a helium atom. An alpha particle only needs to scavenge a couple of electrons to become helium. (We're speaking of helium-4. The isotope helium-3 is not produced this way and is very rare.)
Helium produced this way migrates upward toward the Earth's surface. After it enters the atmosphere, helium diffuses into space relatively fast, in a million years or so.
The same rock layers that trap petroleum also collect other gases, including helium. Some producers of natural gas can do a decent side business in helium, because gas in the ground may contain as much as 7 percent helium, or as little as none. This reflects the amount and age of uranium/thorium-containing materials beneath, the permeability of the rock, the quality of the rock barrier above the gas and the amount of other gases present.
Producing Helium
Raw gas from the ground is mostly methane, which is the part we burn, but in addition to helium it also has nitrogen, carbon dioxide, neon, hydrogen, and water vapor that degrade the quality of the methane. Upgrading natural gas is a process of filtering, scrubbing and cooling that removes almost everything else to yield three streams of material: methane with just 4 percent nitrogen, waste nitrogen, and crude helium. The crude helium byproduct, about 70 percent helium, is then sold to refiners.
The United States is lucky to have more helium-rich gas resources than anywhere else in the world. That and a few accidents of history have made this country the dominant supplier of helium for many years. Helium's uses began in the early 1900s with its role as a lifting gas in lighter-than-air craft (and your party balloons), but it also quickly found favor as a refrigeration gas, a supercold liquid for applications of superconductivity, an inert atmosphere for specialty welding and other roles.
In the long term, helium will rise and fall with the fortunes of the natural gas industry. Producing helium is an energy-intensive process, and energy costs strongly affect world prices. On the other hand, higher helium prices make exploiting lower-quality gas deposits more profitable. And adding complexity to the helium market, new helium production plants are being built outside the United States. As American helium begins to run out, new sources will arise in geologically similar areas.

