There are plenty of information online about how to wire an amplifier or, more often, how to get rid of hum. You can even find multipage presentation with layout suggestions. Instead of prescribing a specific layout, I'd like to summarize my experience in a more concise and flexible way:
1) Safety first. Always connect the chassis to the safety earth on the power inlet unless you know how to make a Class 2 compliant isolated power supply and wiring.
The idea is that should insulation fail, there must be protection for the user touching exposed metal parts. Connection to the safety earth makes sure those metal parts are safe to touch. Class 2 makes sure that even if insulation fails, another layer of insulation keeps protecting.
As a compromise, the chassis may be connected to the safety earth via a "ground breaker", usually a 10ohm or so resistor, a NTC thermistor, or via a couple of sturdy anti-parallel diodes.
2) Use a balanced connection into a differential input were possible. If you have to use differential input with single ended output, use a balanced cable that connects the "cold" wire to the RCA shell at the signal source.
If using XLR connectors for balanced connection, connect pin 1 of the XLR (the shield) to chassis, not to the circuit / PCB / "ground".
A word on terminology: any voltage is "differential" as it is measured between two points. Let's call them signal (or "hot") and reference (or "cold") points. "Differential input" here means having explicit reference point connection. In contrast, single-ended connection implicitly uses some "ground" as its reference point. "Balanced connection" means equal output impedances and equal input impedances for both signal and its reference. A connection can be differential but unbalanced.
A balanced connection is usually impossible with (unbuffered) LM3886 based amps, as they need to ground their reference input for stability.
3) If only a single ended (that is, local "ground "referenced) input is available, make it differential by e.g. using input transformers, then use balanced connection as above. It can be expensive but works great. I used Lundahl with excellent results, but Jensen, Sowter, Edcor will all give you a pair of suitable transformers.
4) If a balanced connection is not possible or not desirable, use separate power amplifier for each channel (monoblocks) or separate power supplies for each channel ("dual mono") and connect the input RCA connector's ground (outer shell) to the chassis via an RC network (100nF, 100 ohms in parallel) to keep out of the box the RFI that’s been picked up by the RCA cable.
5) If the inputs are single ended and the power supply is shared, there may be a problem as each power amplifier channel with have its local signal reference aka "ground" riding on whatever voltage drops on the wire connecting it to the common point at the shared power supply. Each channel will then have slightly different reference, which will manifest itself in hum and/or extra distortion when both channels are connected to the same signal source (e.g. preamplifier). This sometimes is called "cross channel ground loop". There is one solution and couple of workarounds.
5a) The solution is to use a signal source that uses your amplifier's local "ground" as reference. One way to do it is to use an output transformer, which is similar to (3) above. Another is to use a ground sensing (or "ground cancelling") output. Our balanced volume controls can be configured to provide ground sensing.
5b) One workaround is to connect the reference ("signal ground") input of each channel to the local "power ground" not directly, but with a low value (say 10ohm) resistor - some amplifiers have this resistor built in on the PCB. The effect of it is that both channels of your power amp will have their signal reference connect to the signal source via your RCA cable, but to the "power ground" (which is a source of noise) via that resistor. The noise therefore will be divided by the divider formed by the resistor and the wire. A large value resistor would provide better noise rejection, but may reduce the stability margin of the amplifier.
However, most LM3886 amplifier have the signal reference connected to the local power ground directly.
5c) Another workaround is to connect local reference grounds of each channel together by a short, thick piece of wire.
6) Wire any signal and its reference together at all times. If the reference for both channels is the same, wire that reference and both channel signals together. Use twisted pairs (shielded or not) for signals.
7) Make sure that any power supply current (AC or DC) runs tightly alongside its return current - e.g. Live and Neutral on the mains side, or V+ and PG+ wires on the DC side are wired together. Twist power supply wires (both AC and DC), including transformer leads, and take them away from signal wiring as far as possible.
8) Experiment, preferably looking at the FFT of the amplifier's output (you'd need a sound card and some software for that) before committing yourself to the final layout.
9) Disregard grounding gurus, including myself especially if what they are saying is unclear or doesn't make sense to you. The topic of grounding is very much misunderstood, I believe, and I certainly do not claim to be an authority at this. Quoting Nelson Pass, "This being the entertainment industry, I hope everyone is having a good time."