First of all, you need to set up your phone in "expo mode" for recording locations on the plateau reliably. This is not just some technical settings, it also means a particular style of useage whch you need to learn.
The entrance to a cave significant enough to get a number and a survey will eventually be marked by a numbered tag attached to a spit. This will then become the primary survey station - ie. the point where an underground survey will start, and the point to which a surface survey should go. It's worth thinking about where you would put such a tag right from the start. Unlike the first rigging bolt (often used as the first point of a survey in the past) it should be sited with a particular view to its visibility and accessibility without having to put on SRT kit. If such a point has a clear view of the majority of the sky, then this is the point to use for a GPS fix too.
If however, you are dealing with a cave at the foot of a cliff, or otherwise with a restricted view of the sky, then choose instead a good landmark with a wide, clear view of the sky, and with at least two survey shots of the entrance.
Yes, you will have to manually do a surface survey leg using your survey instruments between the GPS point and the cave entrance tag station, and record that in your cave survex file.
Since 2018 we have differential GPS which renders historical advice obsolete (e.g. Wookey's 1996 article) but altitudes are still always inaccurate and GPS devices don't generally tell you how inaccurate they are. Also phones are now much more complicated than the dedicated GPS devices used in the past. It is now the phone itself we have to worry about, not just GPS. Phones try to be "helpful" these days and do not tell you what they are doing.
Once you have chosen your point, mark it in some way (could be a spit hole or a cairn, for example - we don't use paint any more) and place the GPS on the point. Don't build a cairn, they don't last for decades and we have survey stations that provide permanent locations. Give the GPS device a minute to get a fairly good fix (the first figure reported may be quite a way out is you have been moving). Then mark the point as a waypoint (dedicated GPS devices or GPS apps only).
If you're feeling really keen and have a dedicated GPS device or sophisticated GPS app, you can set it up for averaging, which gives a more accurate fix – some GPS receivers support this automatically, and with others you can just leave it recording a track log, then record another waypoint at the same place just before you leave so it's clear to someone examining the track log when you actually left.
While the GPS is averaging your location, you can do something useful (like rigging the cave, doing a surface survey from the GPS point to the marker spit, looking for other caves, or even having lunch!) Remember to stop the waypoint averaging before moving the unit or changing the display page. Take a photo of your GPS point showing at least one of your cave entrances too.
We all use the same coordinate system WGS84 these days, so the extensive discussion on coordinate systems has been moved to a different page. If you are really interested you can read Olaf's articletoo.