I have travelled extensively in China and have my share of self portraits from along the way - usually taken WITH locals rather than by them. I uses a DSLR almost exclusively (Minolta / Sony 5D, 7D, A700, A77) - these are medium to heavy compact DSLRs - the answer below would still apply to an eg D4 but with more difficulty and would be much easier with a point and shoot.
One option for self portraiture & scenery is to use a flexible tripod - often referred to by the name "Gorrillapod" [tm]. These are light and compact and have an additional less common uses as an arm length extender - see below.
Gorrillapod: Gorillapod is a brand name for a flexible leg tripod which may be used to provide a "stable" camera base in unconventional situations. A vast range of imitators and copies are now available so I'll use the tern "flexible-tripod to refere to anything similar. As can be seen in the photo below - the tripod can match uneven surfaces PLUS the legs can be bent around supports.
[<- Wikipedia CCCSA licence. -> ]
Some VERY unconventional support means are possible.
A wide range of great ideas for using a gorillapod
With a DSLR held reversed at arms length , with suitable practice you can achieve reasonably good portraits with one other person, acceptable with two others, getting frenetic with three and somewhat hit and miss above that level. Such photos may include background :-). The aim for me is for the contact/ice-breaking ability, the record, the general fun and the ability to send a photo to them that we can both identify with.
I'm less concerned with "me + view" photos - if I have the photo I know I've been there :-).
BUT for one person and scenery you can get quite good results with just holding at arms length. These can either be with you occupying about 20-25% of frame anywhere in frame or, quite useful, you turned side on at one side of the frame, but looking at camera so the scene is dominant but you are present. This is useful in that it allows cropping out of the "you" element latterly if desired.
To achieve the above you need to find a way you can comfortably hold your camera reversed and operate it to focus at 1/2 pressure and then release and you need to get used to what framing you will achieve. My A77 rear LCD can be positioned above the camera and facing forwards so I can see myself and others and scenery when taking photos this way BUT I very seldom do this as it works well enough blind.
It is easy enough to position the camera so that the holding arm is not visible and indeed so that most people viewing the photo do not realise from looking at it that I have taken the shot myself.
Focal length, focusing, depth of field, other: I usually take this sort of photo at 18mm on an APSC camera = 27mm full-frame equivalent. This is mainly because the walk-around lens I usually use starts at 18mm and has zoom lock - which is useful when operating one handed. ~=30mm equivalent is well below the classic portrait optimum focal length and facial features will arguably look somewhat different but I consider it entirely acceptable for the purpose when the camera is held at arm's length.
I'm usually aiming for the people in the foreground and can autofocus as required except when the arm-extension tripod is used. Aperture needs to be set to allow depth of focus to match your requirement.
Longer arms: A DSLR is a heavy beast. A light mount is liable to have difficulties with the weight. Where I feel I need somewhat more reach I use a clone "Gorilla Pod" tripod mounted to the camera tripod mount and with all 3 legs bent forward to make a handhold. This has proved adequate so far. The camera shutter release cannot be operated directly when it is on the far end of a gorillapod. You could use a cable release, but I simply use the cameras's 2 second timer - swing camera to where you can reach the shutter button, press button and swing tripod into position. Focusing needs to be manual.
I'll post some landscape / distant targeted samples or links to some later.
These are a very mixed bag. For me the picture is only a component in the "fun" as above - many of these could easily have larger depth of focus and/or better exposure. Some have flash obscuration by lens hood due to use at 18mm focal length. I'm often somewhat less in focus than the rest of the group. Framing is variable and interesting.
I'm very happy with them. Others would want to take more effort over "getting them right" photographically and it would be easy enough to do. The shots from outside the train use a flexible tripod arm-extension with 2 second timer. The rest are almost all hand held at arm's length. For the 3 people with a laptop in a Chinese company dorm photo camera may have been on a window sill. If anyone is desperate enough to actually view these life size you need to save the Imgur image and then view it. Just using "open in another tab" gives you smaller version.
These 4 hand held at arm's length. Quality of image was never the primary aim here - but these were cut and pasted from a Facebook album - sure to ensure a low quality end result :-).
1 2 Xian, Xian
3 4 Dieng Plateau (middle of Java), Xian.