Sometimes your data is vector formatted (point, line, or polygon), but it is not the right kind of vector for a particular type of analysis. Or perhaps you need to split a vector in a particular way to facilitate some analysis or cartography. Thankfully, all vector formats are related, lines are two or more connected points, polygons are lines whose first and last point are the same, multipolygons are two or more polygons for the same record, and rings are nested polygons where the inner polygon outlines an area to be excluded. This recipe covers how to convert between the different vector types using built-in QGIS methods.
To convert points to lines or polygons, you will need a shapefile with an ID column that has a single value shared between the points of the same line or polygon. In the following example, we will use census_wake_2000_points.shp.
You will also need to install and activate the Points2One plugin. Refer to the following website for how install plugins, http://docs.qgis.org/2.8/en/docs/user_manual/plugins/plugins.html.
The following instructions show four different conversion methods, depending on the starting data and the end data type. All of the tools are in the Vector menu:

Start by loading the census_wake_2000_points.shp layer.
Converting to simpler types from more complex ones is fairly straightforward in simple cases. Lines are just multiple points connected together and polygons are lines that start and end with the same point. So, it's pretty easy to see how to deconstruct one geometry to simpler geometries.
It's building up from points, which is a little trickier. In a line with three or more points, you need to make sure that you have them in the correct order; otherwise, you'll end up with a squiggle. When going to polygons, this can create bigger issues by leaving you with invalid polygons that self-intersect. So, it's really important to order your points in your source table in the same order that they will be combined. Reordering your data can be somewhat tricky. The Points2One plugin now includes a sort order option; to use this, make sure that your attribute table has a numeric column with the order of the points specified per group (you can restart the numbering at 1 for each distinct grouping).
You can also split or combine multipolygons with the Singleparts to Multiparts and Multiparts to Singleparts commands.
When things get really tricky, you may need to switch to editing the shapes by hand or custom scripts. A good example of this is when you want a polygon with a hole in the middle. If you do go the route of editing by hand, make sure to turn on snapping so that your lines are automatically snapped to existing points. The official documentation on snapping can be found at http://docs.qgis.org/2.8/en/docs/user_manual/working_with_vector/editing_geometry_attributes.html#setting-the-snapping-tolerance-and-search-radius.
The Editing and Advanced Editing toolbars and additional editing related plugins offer the ability to manipulate particularly tricky geometries, one at a time, if you need to.