We develop an operational approach for reconstructing the quantum theory of qubit systems from elementary rules on information acquisition. The focus lies on an observerOinterrogating a systemSwith binary questions andS's state is taken asO's `catalogue of knowledge' aboutS. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions. Four rules are imposed, asserting (1) a limit on the amount of information available toO; (2) the mere existence of complementary information; (3)O's total amount of information to be preserved in-between interrogations; and, (4)O's `catalogue of knowledge' to change continuously in time in-between interrogations and every consistent such evolution to be possible. This approach permits a {\it constructive} derivation of quantum theory, elucidating how the ensuing independence, complementarity and compatibility structure ofO's questions matches that of projective measurements in quantum theory, how entanglement and monogamy of entanglement, non-locality and, more generally, how the correlation structure of arbitrarily many qubits and rebits arises. The rules yield a reversible time evolution and a quadratic measure, quantifyingO's information aboutS. Finally, it is shown that the four rules admit two solutions for the simplest case of a single elementary system: the Bloch ball and disc as state spaces for a qubit and rebit, respectively, together with their symmetries as time evolution groups. The reconstruction for arbitrarily many qubits is completed in a companion paper [P. A. Höhn and C. S. P. Wever, Phys. Rev. A 95 (2017) 012102] where an additional rule eliminates the rebit case. This approach is inspired by (but does not rely on) the relational interpretation and yields a novel formulation of quantum theory in terms of questions.