Try the "Explode lines" from the Processing Toolbox (Ctrl+Alt+T) will split all lines at their vertices to separate lines.
Menu Processing -> Toolbox. Type "explode" into the search field to find the function. Select your line layer from the dropdown and start. This will produce a new layer.
Selecting one or more lines from the line layer will produce a splitted layer with only these features, discarding the rest.
Note: As QGIS is moving fast, all infos below are outdated already.
I think Explode lines would be the the noob-solution through the
QGIS Geoalgorithms > Vector geometry tools > Explode lines. Unfortunately, it does not seem to work at the moment,
i get an error message only.
Traceback (most recent call last):
File "path/.qgis//python/plugins\sextante\core\GeoAlgorithm.py", line 145, in execute
File "path/.qgis//python/plugins\sextante\algs\Explode.py", line 58, in processAlgorithm
features = QGisLayers.features(layer)
NameError: global name 'layer' is not defined
A working solution is the
Split Feature-Plugin from the
"contributed" repository, which does the job for me.
In general I prefer sextante functions over separate plugins, cause
the workflow with sextante is so much faster and produces no
junk-files of intermediate steps (provided it works).
EDIT: Unfortunately, a lot of plugins were not moved to the official plugin repository yet, but are still only available through
the "contributed" plugin repository:
http://pyqgis.org/repo/contributed, which was removed from the default
repositories list with version 1.8.
There you can download them individually and unzip them in your
.qgis/python/plugins folder OR you add this address to your plugins
Plugins -> Fetch python plugins -> Tab "Repositories" -> Add ... -> enter a name and the url.