How Can You Distill Water From Muddy Water?

To separate water and mud, you would not really need distillation. You can simply filter the mud off. However, there might be dissolved substances in the mud water that would not come out of the solution by filtering alone. You can employ distillation for that.
To distill mud water, you need to filter it first any way because the suspended solids in the mixture would otherwise hinder with distillation.
For the distillation, you would need:

Boiling flask
Conical flask
Liebig condensor
Thermometer
Bunsen burner
Tripod stand
Cast iron base with support and clamp

Now connect the apparatus. Put the water in the boiling flask. Place the flask on the tripod stand under which you should place the bunsen burner. Then put a thermometer in the flask and connect it to the liebig condenser. The liebig condenser should be positioned in a way that it slants down towards the collecting flask which you put at the other end of it. You can achieve the desirable height and angle by adjusting the clamp on the stand. Fill condenser with cold water.
Now, light the bunsen burner and weight till the water starts to boil. Check that the temperature does not rise very high. After a while you will notice a liquid collecting in the conical flask you have placed at the and of the condenser. This is your water distilled from muddy water.
I cannot say though that this is as good as the distilled water we use in labs because
a) Many distillations would be needed to achieve that amount of purity
b) There might be other liquids in the mud water mixture that boil before or with water. These would also be present in the water if that is the case.

There is an interesting powerpoint presentation on distillation that I found which might interest you:
DistillationLab
I think it would make it more clear as to how you should connect all the apparatus here.

Well to distill clean water from muddy water you just have to put it in the right position and you sit it in the sun to evaporate and condense.