Our ability to directly relate results from test-tube biochemical experiments to the kinetics in living cells is very limited. Here we present experimental and analytical tools to directly study the kinetics of fast biochemical reactions in live cells. Dye-labeled molecules are electroporated into bacterial cells and tracked using super-resolved single-molecule microscopy. Trajectories are analyzed by machine-learning algorithms to directly monitor transitions between bound and free states. In particular, we measure the dwell time of tRNAs on ribosomes, and hence achieve direct measurements of translation rates inside living cells at codon resolution. We find elongation rates with tRNA^Phe that are in perfect agreement with previous indirect estimates, and once fMet-tRNA^fMet has bound to the 30S ribosomal subunit, initiation of translation is surprisingly fast and does not limit the overall rate of protein synthesis. The experimental and analytical tools for direct kinetics measurements in live cells have applications far beyond bacterial protein synthesis.