From the late 1970s through the early 1990s, a lot of mainstream guitar playing was based on the notion that more was always better, but playing the most notes in the shortest amount of time would automatically translate into supreme six-string wizardry.
Meanwhile, away from the public eye and the willful instrumental ignorance put forth by many punk and alt-rock bands, the total opposite idea gained a lot of steam: maybe less was more, and maybe no guitar would be totally awesome.
Somewhere toward the latter end was a school that saw the instrument for its minimalist possibility rather than for its sonic brute force. With the right treatment and the right attack, a guitar could become a textural instrument instead of (or, in some cases, in addition to) a melodic one, although in some cases the two mutated into each other, as the space created by textural playing created infinite room for berserk shredding. David Gilmour used this dichotomy to perfection on Pink Floyd's 1979 classic "Comfortably Numb," and The Edge fully exploited this use of textural guitar on the title track to U2's The Unforgettable Fire. Other lesser-known but still notable examples of the space guitar attack are David Iscove's work on the You Go Now album by Chroma Key and Buckethead's ninth-chord patterns on "The Interworld and the New Innocence" by Praxis.
Although the mechanics of actually playing to such a style are entirely dependent on a guitar player simply resisting the temptation to touch the instrument, the sound itself has historically been the product of a few choice pieces of outboard gear.
At the absolute most basic level is the use of some type of echo or delay. Some studio engineers like to use these effects only to make a guitar track sound fuller on a recording, but in a live setting such an effect can turn even the most simple of riffs or licks into an infinitely decaying echo of itself. In the studio, software plug-ins often handle the processing duties for a number of reasons. First, they allow infinite experimentation on pre-recorded tracks and allow the guitar player to focus on what they're playing rather than what it sounds like. Software-based delay also reduces the level of line noise and decibel reduction on a guitar track, as fewer cables are used connecting pieces of hardware.
In a live setting, however, most guitar players prefer the on-the-fly flexibility and simplicity of setup involved with hardware-based delay. Like most other effects, these can either be in the form of rack-mounted modules or as the standard stompboxes and pedals. The two accomplish the same general purpose, although in-line pedals have the notable advantages of being considerably less expensive and easier to turn on and off while still playing. As an example, a bottom-end Boss rack-mount delay module will set you back at least $100 used, while the same Boss mechanism in pedal form can be had for around half that.
Most delay pedals also include a "reverse" feature, which will record the guitar output in short bursts (usually a few seconds at most) and replay it backwards, either in isolation or on top of what was normally played.
The second element is variable volume, and this can be accomplished in a number of ways. The first and most obvious is through real-time adjustment of volume knobs during playing. This (obviously) requires the least amount of external support, but also requires some quick work with the hands; having one handing adjusting the volume means it's no longer available for either fretting or picking, so anything beyond open strings will demand extra-hard fretting. This not only ensures maximum amplification of the volume swell, but also makes room for the maximum range of possible variations in volume.
Dedicated volume pedals also exist, and many guitar players prefer to use these in lieu of constantly turning the knobs on their instrument. In the case of guitars with multiple independent pickups, this becomes especially important as either all volume knobs must be turned simultaneously or else pickups must be switched between, effectively undoing the whole reason for having multiple pickup controls in the first place. Such pedals can be found for as little as $30 secondhand, or upwards of $200 for something along the lines of a vintage Bigsby pedal. Some digital delay modules, such as the digital rack pieces by Line6, include a volume swell feature that can be added to the delay.
The last trick in the common space guitarist's bag is the use of artificial sustain, accomplished through either a dedicated sustain module or a little toy known as an E-Bow. The E-Bow is actually used in place of a pick (or fingerpicking for you classical guitarists), and instead of striking the string, the guitar player creates a magnetic field around the string and pickup, forcing the guitar string to vibrate perpetually. This in turn creates a sound for the pickup to transmit, but also does it without the sound of the pick actually hitting the string, thereby creating an infinitely-held note.
One of the great examples of this at work is Robert Fripp's lead guitar line in the song "Heroes" by David Bowie. By holding the E-Bow steady, Fripp was able to track an entire song's worth of guitar using only left-hand fretting. The string is also forced to vibrate much faster and more widely than it would under normal picking conditions, thus creating the louder and fuller sound than with a standard plectrum. By raising and lowering the E-Bow over the string, the player can also improvise volume swells without the use of a pedal, and can create them much more smoothly than with simple volume knob adjustments. Like any other effects-based school of playing, it's less a case of knowing what to use as when and how to use it. Robert Fripp and David Gilmour are certainly held in high esteem, but chances are more people have said "he's a good guitar player" than have said "I really admire the way he manipulates outboard guitar processors." The idea is to know the difference, and to play to a point where it is not just the note (or pattern or effect) that matters, but its presentation. To paraphrase an old saying: the end result is always the same, the rest is just details.