Effects that affect dynamics or distortion are sensitive to what is being sent into them, compared to non-dynamic effects. Be aware of how ordering effects matters, and experiment with each effect before or after a compression or distortion element. For instance, the whole section on distortion character was mostly about how the way a signal is EQ'ed impacts how distortion will operate. EQ before distortion sounds completely different from EQ after distortion. This equally applies to Wah pedals, phasers, choruses, and other effects. On the other hand, certain effects will operate virtually the same and have negligible impact on other effects independent of where it occurs in the effects chain, such as a pitch shifter.
The best advice is to experiment, but here are some general tips:
The general consensus is to make this the first effect in your chain. There it will simply mask your pickup noise when you are not playing. It has the most impact on tone at the end of the chain but can lead to unnatural sounding cut-off on notes. An interesting place for it is after a compressor but before distortion. Sometimes you can use two on each side of a compressor/gain stage to tighten up how effectively it works. This is how Periphery gets their very punchy tone, going quickly from searing power chords to complete silence. See also: Noise Gate.
Note that the signal directly from your pickups is going to by the most dynamic, which makes it best for dialing in gate settings. If you only place a gate after some kind of compression, it will be difficult to find settings that let only let your playing through and not noise.
Generally, you get the expected swooshing sound behind your distortion phase, but placing it beforehand can give a very difficult to describe but interesting sound. I kind of like it in this position, because it has less of a swooshing sound to it, which I find detracts from the actual music. It also makes your distortion character change, which makes it a bit more interesting, especially if you're playing a very repetitive part, such as straight palm-muted single notes (listen to Van Halen's Unchained). I use mod effects in both positions.
As mentioned in Dialing in Distortion Tone, EQ before distortion has a much larger effect on how the distortion operates than how the frequency response is changed. I generally use EQ before the amp/distortion to sculpt the distortion character, while I use EQ after distortion to dial in the desired frequency response in my final tone.
I don't know how anyone gets away with putting delay before a distortion phase. The distortion will compress it and cause the delayed signal to be just as loud or nearly as loud as what you are currently playing, sounding like two guitars fighting for space, playing different things at the same time. People have said EVH put his delay in front his amp distortion, but I can't get it to sound right. I think they're wrong and his echoplex was being used for tonal changes, not actual delay.
I generally put my delay and reverb last (or close to last) in the chain. I don't think it matters which goes first. Occasionally I'll use two delays.
I like these in front my distortion phase usually. A whammy effect especially sounds more like a real whammy bar that way. Harmony pitch shifting I like behind my distortion - then it sounds like you're playing with another guitarist or double-tracking it. When in front, it sounds more like you're playing double-stops. Experiment with the mix when pitch shifting, especially when you put it in front your distortion - low settings will subtly change your tone rather than sounding like you're adding another track at a lower volume.