The main difference with a surface survey is that you can see, and are not constrained by passage walls. The lack of walls may mean that all survey points are on the floor, which can be a pain. It is useful to use one or two "survey staffs", which may be as simple as a stick shoved in a grike, or a photographic tripod which is handy. Make sure not to place a compass too near anything made of steel! An aluminium pole (old tent pole, ski stick or any odd bit of tube or angle) is light and effective. Making it a useful length (eg. 1m or 1.5m) means it can double as a ruler for measuring features.
Surface survey legs tend to be longer than underground ones, so errors from poor compass/clino/distoX angle readings are bigger. In good light you may find it easier or get more consistent results by sighting the compass with one eye rather than two. Remember to do this consistently, and use the same method when doing your calibration. For better accuracy, you should really keep the survey legs short (6m gives a compass/clino error comparable with a 5cm station position error). This makes the survey take much longer, and maybe more prone to recording errors, so a good compromise is to keep legs down to 15m or less, which also makes sketching a little easier.
Using a distoX above ground does make it hard to see the laser spot in bright sunlight of course, which limits the length of legs (except at dusk).
Don't neglect sketching! Cold, exhaustion and call-out times should not be such a restriction on surface surveys, so don't do a rush job (it is best not to do surface surveys when the weather is awful:-). A good surface sketch makes caves easier to find, possibly saving future cavers from repeating your bearings to find the entrance. Eventually such sketches will build to a map of the area, showing which bits have really been looked at.
It is conventional to survey to the cave marker tag, where there is one (and you could always drill a spit for one, and survey to it). Failing that, the centre of the painted number or middle of the "+" sign, or the first bolt of the rigging (remember that we are no longer allowed to paint marks on the plateau surface). Make sure that you record what is used, and its height above/below the "surface".
If you do run out of time, make sure that your final survey point can readily be found again, for example a drilled hole in a prominent boulder (take a photo). Consider going back a few legs if it will give you an easier to find end point - better to lose one or two legs than have to redo the whole survey!
All features of speleological interest should have their position recorded exactly. These days (2018) a long-average (200+ readings) GPS location is fine (see GPS for entrances) in most parts of our caving area. This usually means using a handheld GPS device rather than a phone unless you have a particularly good GPS app which provides an averaging function.
If you are close to a big cliff, or almost inside an overhang, then an averaged-GPS will be good (~ 2m accuracy) for latitude/longitude but appallingly misleading for altitude. In some parts of our area, such as the steep cliffs of the Weisse Wand near Schnellzughöhle (as seen in the photo at the top of this page), altitude is important for route-finding so GPS becomes surprisingly much less useful for re-finding locations. Before you use GPS you really should read GPS for entrances. There is more about GPS altitudes in Olaf's article on GPS in Austria.
Without GPS we need an old-fashioned survey location using fixed points with a minimum of two bearings on fixed landmarks (see taking bearings page for how to do this and for pictures of the various peaks we use).
Anything which gets a number (e.g. 2018-ad-01) should eventually be linked into an existing surface survey. The number (on a metal tag) will be attached to the cave entrance with a bolt, so it is useful to drill a hole for this (and place the spit if possible) early on, so you can use that point as the start of the underground or surface surveys. Always fix new stuff with a GPS (use waypoint averaging) as even if this is not full survey-quality it does prevent things getting lost. There is a separate manual page for using GPS for entrances.
If your new cave is near a well-documented one, then a short connecting survey from one to the other is straightforward. The point on the cave should always be accessible without caving gear. Usually this will be the cave marker tag (or the spit you have placed for one, or hole drilled for it). If there is just a hole, it is as well to mark it with a bit of paint so it can be found again. Failing these, a well-documented spot which can be found again is essential - the first bolt of the rigging or part of a painted number.
The surface is now becoming laced with a network of surface surveys of different vintages and qualities. As these build up, good sketching means a useful scale map can be drawn, which in turn means you can look to see where the nearest existing fixed points are to your cave. The best fixed points are the ones fixed by accurate (laser theodolite) survey by the Austrians, commonly known as "laser points". Next best are surface surveys taking a short route from these points.