I think he refers to this:
https://www.pjrc.com/teensy/external_power.html
A simple "battery" in this case would mean 1.5V (nominal), in 4-series, and adapter would then refer to e.g. buck-converter to drop the 6V (nominal) down to 5.5V or so (to allow a bit for the diode forward voltage). Such setup (with buck-only converter) would perhaps leave some juice in batteries in the end, but it would certainly be an easy setup on the battery side of things. Buck-boost-converter would perhaps work better..
It seems that Teensy 4.0 (and 4.1) have similar Vin vs. USB-power setup as shown on that guide page, but the pads are in different location. Check the two large pads near the bottom left corner in this image
https://www.pjrc.com/teensy/dimensions_teensy40_photo2.jpg, or the top-right corner in "Teensy 4.0 Back Side" pinout reference card (which clearly mentions the "cut", although not as clear about where to cut exactly: between the pads).
The diodes are needed only if you want to power the Teensy both with battery and USB; i.e. if either one (or both) is around, things work. If you want to use only the external/battery power, then only the cut is needed. Adding one diode between battery and Teensy is still recommended (the last part of the guide) to protect a bit from accidental reverse polarity connections.
If adding both diodes:
A diode would be added between those (cut-separated) pads in the same way like in the guide. The cathode (stripe-end) of the diode connected to the pad closer to the Vin-pin. And similarly, another diode between battery plus-side and Vin-pin, cathode/stripe on the Vin-pin end.
1N5817... hmm.. certainly does the job, but I got interested if there would be something better. Alas, in the through-hole component selection, not really. And in the surface mount selection, plenty of better choices, but the pads on Teensy are not designed for direct SMD component placement (they are too close to each other).