With KDE 4 atleast you can adjust the font sizes (and/or DPI settings) in 'Application' > 'Fonts'
To scale some other parts of the display, you can also change the icon size at 'Application' > 'Icons' as well. This is the method suggested for doing this in the Arch Wiki
Note you will need to restart the desktop and applications for it to take effect.
Another method (from the KDE Wiki), is to configure the X DPI settings:
Ideally the screen size (width and height of the monitor screen) is
automatically detected using the monitor's EDID information. This may
not work correctly or not be to the user's preferences. KDE currently
lacks a convenient way to scale everything uniformly. Such a feature
would also help to test proper scaling behaviour.
Modify the X server's settings. In
Option "UseEdidDpi" to the monitor section so that
it looks somewhat like this:
VendorName "Monitor Vendor"
ModelName "Monitor Model"
Option "UseEdidDpi" "false"
DisplaySize 464 292
where the display size (width and height) is in millimeters. The DPI
value is then calculated from these numbers and the monitor image's
resolution in pixels. Use smaller numbers than the real dimension to
simulate high DPI (make everything appear larger) or bigger numbers
for low DPI (make everything appear smaller). The X server needs to be
restarted for the changes to take effect.
To make things more interesting, many distributions these days do not
/etc/X11/xorg.conf file, used to configure the X server, by
default. The X configuration is automatically determined each time X
is started. In most cases, this works well and there is no need to
manually specify X configuration information. To create it, run as
Xorg :1 -configure
/etc/X11/xorg.conf and modify it as
A similar method is also demonstrated on AU here.
KDE is made up of large amount of old components, which probably restrict the support available for DPI screens until the components are updated (list of things that need doing here) - some bits may be better in the new KDE 5 though.
However other desktop environments I think have supported HiDPI for a while, such as Gnome (since 3.10), you could try other DEs to see if support is better there. Under Gnome (and probably Gnome Classic as well), you should be able to adjust the scaling setting via Gnome Tweak Tool.
See also: Can Linux deal with ultra high resolution displays?