It appears the only things you can subscribe to (follow) on Medium are collections, and bookmark stories. Medium will notify you when there's an addition to your collections, or if a bookmarked story was edited.

If you go to your profile settings, you can Connect your Facebook account to see the stories your friends write and recommend - but that's the sum of it.

Finally, you can see what certain people publish and recommend in their personal page at https://medium.com/@twitter_handle.

My guesses as to why you can't follow specific writers are:

1. You can follow their twitter handle on twitter already, and see their page, as mentioned above.
2. They haven't gotten around to implementing it yet :).