If you want to download the source code for MakeHuman and/or run from a source snapshot, see the MakeHuman repository on Github.
You will most likely also want some of the commonly used plugins, such as MHX2 and the asset downloader. These can be found on the plugins page.
Extra assets such as clothes, hair and skins
More assets for MakeHuman can be found in the online repository.
You can found old stable releases at http://files.jwp.se/archive/
Related & useful
These tools are not part of MakeHuman, nor managed by MakeHuman, but are often used in the same pipeline.
Blender is an open source 3d modeler, ray tracer and a whole lot else. This is the 3d software/environment that will work best together with MakeHuman
MeshLab is a tool oriented towards processing large meshes and provides a set of tools for editing, cleaning, and converting meshes. This is useful for producing all-quad meshes for example.