Atmospheric attenuation, atmospheric turbulence, geometric spread, and pointing errors, degrade the performance of free-space optical transmission. In the weak turbulence regime, the probability density function describing the distribution of the channel fading coefficient that models these four effects is known in the literature. This function is an integral equation, which makes it difficult to find simple analytical expressions of important performance metrics such as the bit error rate (BER) and symbol error rate (SER). In this paper, we present simple and accurate approximations of the average BER and SER for pulse-amplitude modulation (PAM) in the weak turbulence regime for an intensity modulation and direct detection system. Our numerical results show that the proposed expressions exhibit excellent accuracy when compared against Monte Carlo simulations. To demonstrate the usefulness of the developed approximations, we perform two asymptotic analyses. First, we investigate the additional transmit power required to maintain the same SER when the spectral efficiency increases by 1 bit/symbol. Second, we study the asymptotic behavior of our SER approximation for dense PAM constellations and high transmit power.