Use the split polygon tool to continue dividing the cylinder's end-cap, following the the two-step sequence shown above.
First, place an edge perpendicular to the one you created in the previous step. You don't need to click the central edge, only the beginning and end points. A vertex will automatically be created at the central intersection.
Now, if we continued connecting vertices diagonally, the resulting geometry would be exactly the same as our original end-cap, which would ultimately defeat the purpose of rebuilding the topology.
Instead, we'll place a pair of parallel edges, like the ones shown in step two. Remember to press enter after you place each edge.
At this point, our end-cap is “quadded out”. Congratulations—you've performed your first (relatively) large-scale topology modification, and learned a little bit about how to handle cylinders properly! Remember, if you were planning to use this model in a project, you'd probably want to quad out the other endcap as well.