Inspired by the compute-and-forward scheme from Nazer and Gastpar, a novel multiple-access scheme introduced by Zhu and Gastpar makes use of nested lattice codes and sequential decoding of linear combinations of codewords to recover the individual messages. This strategy, coined compute-forward multiple access (CFMA), provably achieves points on the dominant face of the multiple-access capacity region while circumventing the need of time sharing or rate splitting. For a two-user multiple-access channel (MAC), we propose a practical procedure to design suitable codes from off-the-shelf LDPC codes and present a sequential belief propagation decoder with complexity comparable with that of point-to-point decoders. We demonstrate the potential of our strategy by comparing several numerical evaluations with theoretical limits.