The method n76 describe is fine for the simple tags, but there is a potential problem with relations when you “split/duplicate” a way to represent a dual carriageway.

E.g. public transport routes are represented as relations in which the way is a member. JOSM (or one of it’s plugins) has a method to copy relations from one way to another. This would be easy, but you introduce a oneway. This means that half of the relations should contain the way in one direction and the other half have to contain the other direction.

It’s pretty hard to explain in a few words, so I can understand you might be scared by now. Please don’t, do what n76 described and ask for help here on splitting the relations.