First you have to implement AABB picking with AABB-ray intersection test. Picking an OBB is then achieved by transforming the ray inside the OBB's local space and doing an intersection test with an unit AABB - local ray. Transforming the ray into the OBB local space is done by transforming the ray origin and ray direction by the inverse of the OBB's transformation matrix.
To get a picking ray, you have to unproject your pick position (mouse position) to the camera near and far planes by transforming it by the inverse view projection matrix. Something like this:
vector3 near = vector3(mouse.xy,0,1) * matInverseVP;
vector3 far = vector3(mouse.xy,1,1) * matInverseVP;
vector3 rayOrigin = near;
vector3 rayDirection = normalize(far - near);