Intelligent reflecting surface (IRS) is a promising technology to enhance the coverage and performance of wireless networks. We consider the application of IRS to non-orthogonal multiple access (NOMA), where a base station transmits superposed signals to multiple users by the virtue of an IRS. The performance of an IRS-assisted NOMA networks with imperfect successive interference cancellation (ipSIC) and perfect successive interference cancellation (pSIC) is investigated by invoking 1-bit coding scheme. In particular, we derive new exact and asymptotic expressions for both outage probability and ergodic rate of the m-th user with ipSIC/pSIC. Based on analytical results, the diversity order of the m-th user with pSIC is in connection with the number of reflecting elements and channel ordering. The high signal-to-noise radio (SNR) slope of ergodic rate for the $m$-th user is obtained. The throughput and energy efficiency of non-orthogonal users for IRS-NOMA are discussed both in delay-limited and delay-tolerant transmission modes. Additionally, we derive new exact expressions of outage probability and ergodic rate for IRS-assisted orthogonal multiple access (IRS-OMA). Numerical results are presented to substantiate our analyses and demonstrate that: i) The outage behaviors of IRS-NOMA are superior to that of IRS-OMA and relaying schemes; ii) With increasing the number of reflecting elements, IRS-NOMA is capable of achieving enhanced outage performance; and iii) The M-th user has a larger ergodic rate compared to IRS-OMA and benchmarks. However, the ergodic performance of the $m$-th user exceeds relaying schemes in the low SNR regime.