I am very new to blender, I am trying to create a simple creature, here I try to extrude some legs, but I get this weird distortion where the legs and the body meets when I use smooth shader, what is causing it?
This is an important topology issue, not strictly Blender-related. Basically you have to add some loop cuts, trying to have even quads over all the mesh, then add some others loop cuts to "hold" the edges.
Hover your mouse over the leg, press Ctrl R, scroll the wheel until you get the desired number of loop cuts and confirm with left click. Then do the same near the start and the end of the leg, moving the single loop and confirming. The direction of the loop is dependent by the mouse position.
Experiment with this tecnique and search articles and tutorials on Topology, it's an essential skill for good modeling.