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This paper investigates the passive beamforming and deployment design for an intelligent reflecting surface (IRS) aided full-duplex (FD) wireless system, where an FD access point (AP) communicates with an uplink (UL) user and a downlink (DL) user simultaneously over the same time-frequency dimension with the help of IRS. Under this setup, we consider three deployment cases: 1) two distributed IRSs placed near the UL user and DL user, respectively; 2) one centralized IRS placed near the DL user; 3) one centralized IRS placed near the UL user. In each case, we aim to minimize the weighted sum transmit power consumption of the AP and UL user by jointly optimizing their transmit power and the passive reflection coefficients at the IRS (or IRSs), subject to the UL and DL users' rate constraints and the uni-modulus constraints on the IRS reflection coefficients. First, we analyze the minimum transmit power required in the IRS-aided FD system under each deployment scheme, and compare it with that of the corresponding half-duplex (HD) system. We show that the FD system outperforms its HD counterpart for all IRS deployment schemes, while the distributed deployment further outperforms the other two centralized deployment schemes. Next, we transform the challenging power minimization problem into an equivalent but more tractable form and propose an efficient algorithm to solve it based on the block coordinate descent (BCD) method. Finally, numerical results are presented to validate our analysis as well as the efficacy of the proposed passive beamforming design.