Create you geometry with a sufficient amount of polygons.
Create an armature with however many bones you want. For smooth deformation and easier skinning, it may be easiest to use a segmented bone.
Skin the geometry to the armature. Automatic weights are probably sufficient, especially if using only one deformation bone.
Pose the armature for the desired curve.
“Apply” the armature modifier on your geometry.
I was very vague here since I don’t know how familiar you are with different things. If you need more details about anything, I can elaborate.
EDIT: It might be easier to use as few vertices as possible along with a subsurf modifier and with edge creases. It depends upon how complex of a curve you want. And, when you apply the subsurf, it would result in a great number of polygons where you don’t need them compared to using an armature.