Just a general guide on multi-effects processors.

What exactly is a processor?
There are two ways to look at the processor. One way is as a DSP(digital signal processor) i.e as an effects unit much like a pedal which is inserted at some point in your sound signal chain(eg in front of the amp; Guitar>>processor>>amp). The processor converts the analog signal to digital and add effects to it and then reconverts it back to an analog signal to be sent to the guitar amp.

The other way is as a preamp, much like a mic preamp; Something to amplify a low level signal and add effects to it before sending it to the mixing board, recording device or PA. This way you can record directly without using an amp...

common features/modules of Multifx processors.

Effects/Modulation: this refer common effects like reverb delay and flanger to more exotic ones like slow gear and univibe..
Heres a link for more detailed explanation on various guitar effects.

Amp modelling: The amp modelling simply process the signal to make it sound similar to the sound of a guitar amps. There are a few common amp models found on every processor. These include a marshal plexi model(which is named British stack in a korg 1500g processor), a rectifier model (which is US high-gain on the korg), a tweed model etc. You can check out the webpage of the product to find the list of amp models(hint: they might not give the name of the actual amp but its easy to figure out an example would be "gratifier" for the rectifier).

Distortion/overdrive/stompboxes: models after various classic and famous dist and overdrive pedals.

Speaker/cabinet modeling: Much like amplifier the cabinet add greatly to the overall tone of the guitar. Processors have few selection of cabinet models. One great thing is that we can try different combination of amp models and cabinet models and try to find a unique sounds. Here a link for the amps and cabinet models of the POD X3 live

Microphone modelling: There not just models for different mics but also on placement of the mic. My GT6 has option for mic placement at the centre or edge of the speaker. The placement distance can also be dialed in.

Expression Pedal: Apart from controlling wah models the pedal may be assigned to control various parameters of various effects. eg to control the rate of delay.

FX-loop: High-end processors have FX-loop for adding external pedal/effects units to the signal chain. You can assign the position of the external effect in the signal chain.

How to use Multifx.
Direct recording.
The typical electric guitar sound that we are familiar with is the result of the extensive signal processing by the pedals, various stages of amplification circuitry in the GUITAR AMP and the speaker(s). Now, there is wide range in the tonal characteristics of different amp models and brands because of differences in circuit design and speakers.

For a typical guitar recording using amp the amplified output of the amp, coming form the speakers (the result of the above said components) is mic'ed with usually an instrument microphone and the output is sent to the recording device. This output is the final result and the recorded sound that you can hear on tape or in digital format..
Now that seems like a whole lot of trouble and costly equipment.
Thats where the processor comes in handy.

The processor can take a guitar signal and digitally process it and add the characteristics of PEDALS, AMPS, SPEAKERS, and MICROPHONE and much more, giving a signal that can be recorded directly.

Most processors also comes with USB interface so that you can record directly with minimum latency(delay) and without external interference and noise. For the same recording quality with an amp you would have to spend many times the cost of a Processor.

For effects with amps.
The processor is simply put infront of the amp with the effects you need turned on. You dont usually use the amp models or cabinet models when using with amps.
Another way of using the processor with amp is to put it in the FX-loop, if you amp allows it.
Here more about loop

Another way of using the processor with an amp for more control is the 4 cable method. But it requires that the processor and the amp have FX-loop..

Advantages of the MFX

Cost: Extremely cost effective if you are looking for decent home recording. Similar sound quality would require lot more money if you go for mic'ing. you have to have decent amp, mic, interface, soundproofing etc..even professionals are using processors.
Even for live gigs you can use a processor provided that theres a decent house PA and monitoring. So you avoid having to carry around your amp and breaking your back.

Control over effects/tone: Because you can program presets in the process with virtually any combination of effects, you can have a variety of tones at the press of a button. Imagine if want to go from a clean tone with chorus to a distorted one with delay and tremolo. You would have to dance around if you are using pedals and the only alternative is to get an expensive midi pedal board.

Convenience: Less cables, easy to carry around. And very good for experimenting with effects.

Obviously tonal quality is less compared to analog gear. But technology has come a long way and people are often prejudiced to quickly dismiss processors based on the reputation of old models.

Some good processors.
Low-end: Zoom G2.1u, Digitech RP150,250 They all have usb interface and reasonably good amp models. So are good for home recording.

The best: The POD X3/XT, boss GT10, Digitech GNX4, TC electronics g-major... The POD X3 is supposed to have the best amp modeling of any processor so it would be the best choice for recording. Boss traditionally is supposed to be good for effects, so you might want to consider that it you want to use it for effects with amp. And there is the Vox tonelab LE and the zoom G9 which have a tube preamp stage. I dont know how much of a difference this makes to the tone.

Boss ME50, line6 m13 etc. Thought i'd put in a word of caution about these. I've known a few people who bought the ME series and were dissapointed to find that it didnt have amp modeling. So dont get these if you want to record or want to use amp modeling. The ME is a great unit to use with an amp though.
I don't see the Tonelab mentioned anywhere on here... and it dwarfs any and all competition, especially Pod's...
Quote by ambush_xx
Boss ME50, line6 m13 etc. Thought i'd put in a word of caution about these. I've known a few people who bought the ME series and were dissapointed to find that it didnt have amp modeling. So dont get these if you want to record or want to use amp modeling. The ME is a great unit to use with an amp though.
Nice write-up. IMO rather than writing this caution as a footnote (so to speak), I would talk about these as a category of multifx. Units like the ME-50 are intended to emulate separate pedals on a pedalboard as an integrated unit. Versus the others which are complete modeling units suitable for direct recording or direct into a PA system, as well as guitar amp. Some people prefer the pedalboard paradigm. So it's more informative to describe the rationale behind the design rather than simply point out their shortcomings.
You also left out the Fractal Axe FX. Which is very high end gear.Also power amps designed to work with processors. The arena is a bit bigger then what comes out of the GC handbook.
Dean Icon PZ
Line 6 Variax 700
Dean V-Wing
Dean ML 79 SilverBurst
MXR M 108
H2O Chorus/Echo
Valve Junior (V3 Head/Cab and Combo)
VHT Special 6
Phonic 620 Power Pod PA
Wampler Super Plextortion
Line 6 Pod HD