In this paper, we investigate novel strategies for generating rate-compatible (RC) irregular low-density parity-check (LDPC) codes with short/moderate block lengths. We propose three puncturing and two extension schemes, which are designed to determine the puncturing positions that minimize the performance degradation and the extension that maximize the performance. The first puncturing scheme employs a counting cycle algorithm and a grouping strategy for variable nodes having short cycles of equal length in the Tanner Graph (TG). The second scheme relies on a metric called Extrinsic Message Degree (EMD) and the third scheme is a simulation-based exhaustive search to find the best puncturing pattern among several random ones. In addition, we devise two layer-structured extension schemes based on a counting cycle algorithm and an EMD metric which are applied to design RC-LDPC codes. Simulation results show that the proposed extension and puncturing techniques achieve greater rate flexibility and good performance over the additive white Gaussian noise (AWGN) channel, outperforming existing techniques.