Always consult the official Owners Manuals and Guides first.
Information about the FM3 may be incomplete or wrong, it's being worked on.
Amp and Cab modeling for beginners
Virtual preamps and power amps
Most traditional guitar amplifiers consist of a preamp and a power amp. The preamp usually is responsible for tone and gain, the power amp takes care of amplification and also adds some character of its own to the tone.
The Axe-Fx series and AX8 model both; they are "virtual" guitar preamps and power amps. More than hundred heads, combos and racked preamps have been modeled.
The processors also provide many other effects, they can "reamp" a recorded dry signal, create Tone Matches of real amps and recordings (Axe-Fx only), capture impulse responses (Axe-Fx only), and more.
Using a traditional guitar speaker or full-range amplification (FRFR)
There are many ways to enjoy the sounds from Fractal Audio's Axe-Fx and AX8 processors: headphones, studio monitors, IEM, FRFR monitors, power amps and guitar cabs, etc.
Additional amplification is required to get loud on stage. Usually this means using either a traditional guitar cab with a power amp, or a so-called FRFR monitor.
A traditional guitar speaker will give you the familiar and fairly easy to set up "amp-in-the-room tone". It does limit possibilities, because any sound you will create will be colored by the guitar speaker, instead of using flexible cabinet modeling with its unlimited possibilities. When using a traditional cabinet, Cabinet Modeling needs to be disabled in the processor's setup menus.
To feed the guitar speaker, a separate hardware power amp is required. This can be a guitar-oriented power amp, head or combo (this requires disabling Power Amp Modeling in the processor's setup menus), which add its own coloring to the sound (and decreases the possible tonal variations). More popular: a so-called "neutral" power amp (keep Power Amp Modeling enabled), which neutrally amplifies the incoming signal into the guitar cabinet.
Alternatively, you can opt for FRFR sound reproduction: Full Range Flat Response. This requires a FRFR speaker and an external or built-in "neutral" power amp. Studio monitors are FRFR by nature, as well as some monitor wedges and cabs, and high-quality PA-systems. FRFR systems and direct recording require Cabinet Modeling because there's no real cabinet to put the sound through. The Axe-Fx and AX8 have many built-in cabinet models. They also allow loading additional cabs from disk, known as Impulse Responses (IRs) or user cabs. Note that when you're using an FRFR sound system with cabinet modeling, you'll be listening to the sound of a miked speaker, as opposed to a traditional guitar speaker. An IR / cab model almost always represents the tone of a speaker that was captured using one or more microphones placed very close to the speaker (referred to as "nearfield" or "close-miking"). That's a different sound than that of a guitar speaker at a distance ("far-field"). Because of the proximity of the mic to the speaker, the sound of FRFR produces more highs and lows, and has the characteristics of the microphone baked in. It can take a while to get accustomed to FRFR tone, but realize it's the same tone the audience hears through a venue's sound system and when listening to recorded music.
Make the guitar cut through the mix
Important in general, but especially when playing through FRFR amplification: Fletcher-Munson curve. This is the scientific name for the fact that human ears perceive sound at low volume levels differently than at higher levels. At low volume levels people often turn up treble and bass. The Loudness switch on older home stereo systems does just that. At higher levels those controls need to be turned down to prevent harsh and boomy tones and to prevent the guitar from getting lost in the mix (a guitar that competes with cymbals and bass guitar will always loose that battle), turning up the volume won't help. So always dial in your live guitar tones at gig levels, and remember that the guitar is a "mid frequency" instrument.
Input clipping is not the same as output clipping.
It's okay for the Input LED to "tickle" the red. If it happens all the time, adjust Input Level/Pad in the I/O menu. Be aware that this control is NOT a gain control, it controls the signal-to-noise ratio only and does NOT affect signal level, amp gain or tone.
The Output LED indicates that the signal level in the effects chain is too hot for the digital-to-analog converter. Adjusting the Input Level will NOT solve this. Decrease the level somewhere in the chain, preferably using Level in the Amp block, or in the Output block.
Avoiding parameter paralysis and option anxiety
The sheer number of parameters and possibilities within the Amp and Cab blocks can dazzle the beginner. Therefore it's handy to have a reference tone. The Band-Commander (clean tone) and Friedman HBE (dirty tone) amp models at defauklt settings can serve as such, combined with stock cabinet 103 (Cab block at default settings).