I agree that use of the approach procedure chart is the best and simplest way to brief. The chart acts as a visual aid to ensure you haven't missed anything that's important.
If you are flying with another pilot, the Pilot Flying the approach should brief it; then the Pilot Not Flying should review the chart, ask any pertinent questions, and catch any mistakes or omissions that the briefing pilot made. The most common one I see is failure to brief the charted missed approach procedure, or other MAP as issued by ATC.
If you are flying a single-pilot operation, brief yourself. Out loud. Sounds silly, but for pacing yourself and ensuring that you've covered all the bases, it works pretty well. Just try to keep the pax from hearing you, as they may wonder if flying with a guy who mutters to himself while looking at little pieces of paper was such a good idea.
Ideally, you should brief as soon as you have the ATIS...i.e., as soon as you know which approach to expect. This will usually be just prior to descent, or early on in the descent. If possible, try to get it done before going through 10K, but this is sometimes not possible due to the demands ATC puts on you. Regardless, do your best to get ahead, and stay ahead, of events. As you brief, set up anything that needs to be tuned, if possible. This will prevent overload as things tend to get busier and busier close in to the airport & low down.
Do not forget to get a positive aural ident on any (non-GPS) navaids you will use. This old-fashioned technique will save your life (or your certificate) sometime. A common error is to forget to monitor the navaid aurally when flying an NDB approach.
For your FAR 91 & 135 operations, as you begin to fly to more and more different airports, especially for the first time, include in your briefing the name and location of the FBO and how you will get there from the likely runway of landing. For quick ego deflation, there's nothing like completing a needles-centered ILS to mins, followed by a grease job landing, and then having the tower ask you during rollout, "where ya parking," to which you key the mike and respond, "Uhhh......" The simple act of knowing which way you will turn off the runway to proceed to the FBO will save you a lot of time and prevent the wrath of controllers.
In actual line flying, you can pretty much count on 90 out of 100 approaches being visuals...9 of the remaining 10 will be ILS...that last one will be some kind of nonprecision approach. Lack of recent experience with same, plus complacency, is why so many people bust their a** doing them. Don't let this happen to you.