Try using the nightly builds, they’re more bug fixed and advanced than the 5.1 beta :
http://download.tuxfamily.org/makehuman/nightly/
Extract the archive downloaded of the night build and in the folder click on Update.bat to build the executable correctly as instructed somewhere in their forum (without doing that the executable would not work).
Now launch Makehuman and built a character.
Exported your character as a .mhx file.
The files are saved, at least on my XP OS, in
…My documents\makehuman\exports\
The texture are in your extracted folder :
…\makehuman\data extures\
It’s texture.tif, put it in your …My documents\makehuman\exports\ along with the model.
Now for the Blender part, DO NOT use the import script that are
…\makehuman\importers\mhx
folder
Each time i tried to use one of them, i ended with lots of errors.
Instead use the script that come with a standard Blender 2.56, go into File -> User Preferences
Click on the Addon tab, click on the Import-EXport category.
And there, tick the case that are next to :
Import-Export : Import : Images as Plane
Import-Export : Import : Makehuman (.mhx)
Once you have ticked those case, those addons are enabled.
Close the user preference window now.
Click File -> Import -> Makehuman (mhx) , select the mhx that model name end by 25.mhx as the one that end with 24.mhx is supposed to be for Blender 2.49b.
no need to change any of the default options, just wait until it’s loaded :

Now if you don’t need those clothes to work on the character, you can select them and press delete to remove them.

You now can notice that there are 2 models on top of each other, no idea why, one of those model is named “forsakenMesh : basis”, it’s the one that is slightly colored in pink on the screenshot
It’s UV map correspond to no texture available in the makehuman install, so i have no idea what it is for.
Once deleted you should have that :

Now you can select the armature, go into Pose Mode and start whatever you want.

you can import the hair model (File -> Import -> Wavefront OBJ) if you added them in Makehuman if you want and get them right for the character.
You can render, the texture is already setup.