Laymen commonly wrap the term "drilling" around overly broad aspects of exploration, development, and production. In the industry, that term is more restricted to making a hole in the ground and getting some pipe (casing) cemented into it. For many decades now, for nearly all onshore wells, that casing is cemented into the hole, with cement between the pipe and the producing formation. There are typically multiple concentric strings of casing, chosen and placed for many considerations including government regulations that always require one cemented across all the shallow fresh water (potable or treatably potable) zones.
Connecting the petroleum reservoir to the wellbore and providing for the fluids to flow to the wellhead are "completion" operations.
Where reservoir rock are permeable enough, it might be enough to simply cement pipe above but not across the producing zone. If the rock is mechanically competent, a simple "open hole" completion might be enough (e.g. many old Permian Basin wells into hard limestone and dolomite reservoirs). If the "rock" barely deserves that name and is prone to shed sand into the wellbore, the hole might be supported by a screen or slotted pipe as Dinwar described for his water wells, possibly surrounded by coarse sand (a "gravel pack" completion). Those situations aren't what's at issue here.
Casing and cement are typically "perforated" by shaped-charge explosives that shoot ~half-inch holes through the pipe and cement, a few inches into the surrounding reservoir rock formation. Depending on formation properties, "perfs" may be spaced a few inches to a few feet apart across the productive zone.
The permeability of the reservoir rock at its interface to the wellbore and perforations is generally quite damaged by the operations of drilling (e.g. fluid leakoff into the "sandface"), cementing (duh) and perforation (which amounts to pounding a hole into the rock with a copper-plasma hammer). Usually, that damage is "broken down" by pumping into the perforations, often with acid, with enough pressure to break the rock locally but often not enough rate and volume to extend the cracks very far before the fluid leaks off into the permeable rock. In some cases (none relevant to tight gas reservoirs) it's also possible, but not as common, to evacuate the wellbore somewhat before perforation, so the higher reservoir pressure can flow into the "underbalanced" wellbore to clean up the perfs on its own.
To produce oil or gas or water or molasses, the fluid has to flow through the rock to get to the perforations and wellbore. As the flow approaches the wellbore, it has to converge toward it, increasing the local flux (flow per unit area) and gradient (pressure drop per unit distance). If the rock is "tight" -- that is, low permeability -- even a large pressure drop from the reservoir to the wellbore will induce only a small flow rate. Beside consideration of the rate of return, if that flowrate and well bottomhole pressure are not high enough to lift the fluids -- including any entrained or condensed liquid -- to the surface, the well "dies" (stops flowing).
Hydraulic fracture stimulation is often applied to reduce the resistance to flow from the reservoir to the well (the effect is more "makes the well look wider" than "increases the permeability", but that's a technical quibble only reservoir engineers enjoy). Because the same resistance exists to fluid pumped into or out of the well, fluid is pumped into the well fast enough to raise pressure enough to crack the rock ("frac gradient" is typically near 0.7 psi per foot of depth).
Frac fluid is commonly water-based, especially for larger jobs, though crude oil and diesel are used for some water-sensitive formations. Additives are blended to give desired fluid properties. The fluid may be foamed with N2 or CO2.
When pumping stops, the rock's elasticity will try to close the fracture... so proppant is generally mixed with part of the frac fluid to hold the crack open when it tries to close. Proppant is often clean, well sorted sand, but other materials are often used for their special strength or hydrodynamic properties (coated sand, aluminum oxide beads, walnut hulls...).
Such hydraulic fracture stimulations are not at all new. This is almost always done for onshore "hard rock" wells for many decades now, not just recent "tight gas" wells. IIRC Mr. Halliburton did the first one back about 1932 with 300 gallons of lithium-soap gelled gasoline and a few dozen pounds of sand proppant, in the Guymon:Hugoton gas field. (An interesting project might be to tell those Ogallala aquifer dependent dry-land wheat, cattle, and cotton farmers the gas wells on their land shouldn't be frac'd. Go ahead... I'll wait here.)
What is new-ish is economical application of horizontal drilling techniques and specialized downhole tools to allow multiple, widely spaced fracture stimulations from a single borehole, to facilitate economical production from very, very tight gas reservoirs that would not otherwise be economical to produce. "Frac jobs" are individually designed for each specific well, but for an idea of scale these sort of stimulations involve a handful of "stages" each involving a few thousand barrels of fluid, part of which is pumped with a very few pounds of proppant per gallon.
What's "tight"? Your concrete driveway offers about 3-5% porosity (where gas would live) and about 20 microdarcies permeability (how the gas would get out). Several of the recent shale gas plays score lower on both counts. More conventional gas reservoirs offer around a millidarcy more or less, onshore oil reservoirs are typically a few tens to hundreds of millidarcies, and really sweet reservoirs might offer a whole darcy or two. For comparison, an impermeable matrix with 0.01" fractures every inch has permeability about 54 darcies (54,000,000 microdarcies). (one darcy permeability will pass 1 cm3/cm2/sec of 1 cP fluid at 1 atm/cm pressure gradient)
Below about 3000' deep, these hydraulically induced fractures will be oriented essentially vertical in a direction defined by the reservoir itself -- that is, perpendicular to the least principal stress direction -- regardless of the local orientation of the wellbore. Horizontal "pancake" fractures can occur only at shallow depths where overburden stress is low, or where unusual tectonic stresses otherwise make that the direction of least principal stress.
How far these fractures extend, and how tall they grow, is limited by how fast the frac fluid can be pumped into the well and how fast that fluid leaks off from the fracture into the surrounding rocks. Making fractures more than a couple thousand feet long is extremely difficult, however desirable it might be. Making fractures tall is usually undesirable (because that would connect the well and/or reservoir to unwanted zones), and even more difficult because of the laminated nature of overlying sentiments that can tend to inhibit (but not totally prevent) fracture propagation through multiple zones.
Extending an honest hydraulic fracture up to freshwater sands from a completion at, say, 10,000' deep just ain't gonna happen. If you want to try, you'll run out of location room to park all the tankage, blenders, and pump trucks that would take. You don't really want to try, though... those other zones (freshwater or not) could steal away the gas you want to produce, or dump stuff you don't want into your well (e.g. water, fresh or not).
The issue, then, is where that fracturing fluid pressure is actually applied to subsurface rocks. The high pressure needed to fracture a deep zone is more than enough to fracture a shallower zone... *if* it gets to one. Well casing and its cement seal in the borehole are what keeps that from happening... unless they're not as they should be.