You'd go about it like you did when you snapped to points in [this post](https://gis.stackexchange.com/a/132625/23263)

All you have to change is that instead of choosing to snap to vertexes you would snap to *segments* (or both, depending on your goal).

![enter image description here][1]


  [1]: https://i.sstatic.net/iam07.png