Considerations of the shape of the universe can be split into two parts; the local geometry relates especially to the curvature of the universe at points everywhere, and especially in the observable universe, while the global geometry relates especially to the topology of the universe as a whole — which may or may not be within our ability to measure.
Cosmologists normally work with a given space-like slice of spacetime called the comoving coordinates. In terms of observation, the section of spacetime that can be observed is the backward light cone (points within the cosmic light horizon, given time to reach a given observer). For related issues, see distance measures (cosmology). The related term Hubble volume can be used to describe either the past light cone or comoving space up to the surface of last scattering. From the point of view of special relativity alone, speaking of "the shape of the universe (at a point in time)" is ontologically naive because of the issue of relativity of simultaneity: you cannot speak of different points in space being "at the same point in time", thus you cannot speak of "the shape of the universe at some point in time". However, the existence of a preferred set of comoving coordinates is possible and widely accepted in present-day physical cosmology.
If the observable universe is smaller than the entire universe (in some models it is many orders of magnitude or even infinitesimally smaller), one cannot determine the global structure by observation: one is limited to a small patch. Conversely, if the observable universe encompasses the entire universe, one can determine the global structure by observation. Further, the universe could be small in some dimension and not in others (like a cylinder): if a small closed loop exists, one would see multiple images of objects in the sky.