Calafat is a major crossing point between Romania and Bulgaria. There is a toll bridge across the Danube river to Vidin on the Bulgarian side, but there are no longer any public ferries across the river. Nor is there a bus; the only option is a slow train, walking, or hitch-hiking.
There are four slow (the 107 km trip takes three - three and half hours) Personal type trains daily from Craiova.
There are several buses per day to/from Craiova; travel time is around two hours. They leave Craiova from the station.
This crossing has become troublesome since the bridge was built and the public ferry ceased. Try to hitch a ride across the bridge from the road 1 & 12 junction outside of town. There is a petrol station (Sunny Oil) with a loo but it's on the wrong side of the junction; more luck can be found on the slip road onto road 1 after the junction. Unfortunately, most hitch-hike friendly drivers are not crossing the expensive toll bridge so this method involves some patience. At the border crossing on the Romanian side, it is not too tricky to get another lift although again many drivers are affluent and not interested in picking up strangers.
The city is walkable.