One of the main approaches in the literature is based on offering a consumer a choice between sets of bundles and then using a revealed preference theory framework to infer what kind of utility and demand functions (if any) are consistent with the observed choice behavior.
For example, suppose that we one data observe a consumer able to buy any of bundles $\{A,B,C,D,\ldots\}$. From this set, he chooses $A$. Applying the Generalized Axiom of Revealed Preference, we can place some restrictions on the preferences that could generate this choice. For example, in the below figure the choice of $A$ from the set $\{A,B,C,D,E,F\}$ is consistent with the blue and green preferences, but not the red or orange ones.

Note that this approach works with observational as well as survey data. It has the advantage that much work has been done to understand exactly what can and cannot be inferred from a set of observed data—culminating in Afriat's theorem. A fairly neat introduction to this literature was written by the inimitable Hal Varian: "Revealed Preference".