There are multiple rules.
Keep the inputs away from the outputs. For example, keep the inputs on the LHS and the outputs on the RHS and feed the power in from the top or bottom, keeping any PSU section from invading the signal parts..
Don't run signal traces in parallel, cross them at right angles if absolutely necessary.
Run the power traces as close together as possible, particularly for any class B sections.
Run the ground returns from each section independently, or at least keep the low current returns at the far end of the string and the high current returns close to the ground point. Google 'star grounding'. If you do use a ground plane try to make sure there is an uninterrupted 'line-of-sight' return for each grounded point and that the sightlines don't cross. Sometimes a slot in the groundplane can serve to keep unwanted mingling of ground returns to a minimum.
Keep power supply decoupling caps as close to the pins they serve as possible. Keep the loop area enclosed by the pins as small as possible.
If any transformers or inductors are used, give due consideration to the fields generated by them, amplifier output inductors for example should not be placed inline as the interaction will be at a maximum. Distance is the cheapest isolator.
Don't run traces under IC components or between pins if at all possible. This is of lesser importance in digital circuits, but signal integrity is of increasing importance as clock frequencies rise. Don't locate vias under ICs.
Keep any digital section away from the analog section, with an independent ground plane. Join the ground planes at a single point and consider what currents may pass through that point, organizing the layout to minimize them. Don't use higher frequency clocks if it is avoidable.
These rules are important, but can be modified by other considerations, for example a commercial product may have style considerations affecting the input and output positions on an enclosure, plus there are volume and maybe tone controls, LED indicators, input selectors, etc.
Be prepared to respin a board on the basis of what is learned from the first iteration.
Don't join traces at less than 90 degrees, this is called an 'acid trap'. It increases the difficulty of isolation routing if it is used at some stage. Chamfer all right angle turns. This is of less importance in low frequency (baseband) PCBs, but it's a good habit to get into. Beef up the tracks, as a general rule make them the same size as the component pads. You can use thinner, in some cases it's necessary, but same size as the pin pads is a good rule of thumb.
I'm sure there are other things other people will think of, this is just what occurs to me off the top of my head.
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