In C:S as in real life, congestion is usually generated at the MERGE between two highways (or other busy roads). Plonking down an extra carriageway does not by itself increase merge capacity; at best it just moves the congestion slightly further down the road where the parallel carriageway merges back in (‘the primary merge’). If you want to kill the congestion rather than just move it around you need to take traffic away from the primary merge. In the following screenshot you can see two ways of doing this. On the inner carriageway there is a conventional exit prior to the primary merge. On the outer carriageway there is no exit prior to the merge, but there are lots of extra exits after the primary merge, which means that traffic has reasons to stay away from the primary merge.
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437522895

There is a specific issue with C:S at the merge. Most times you will want to start the new parallel carriageway with a merge between two ramps. Both ramps will often by default merge into one lane of the highway, which creates congestion. To get around this, you should make sure that the ramps at the start of the parallel carriageway come in from opposite sides. When the ramps are coming in at the correct angle for an orderly merge, one will have a left turn arrow and one will have a right turn arrow. If either ramp has a straight-on arrow it is likely that it will actually merge to the left or right and create congestion. Weird, but that's how it works.
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437522773

You generally want to put similar amounts of traffic on the two carriageways so you using all the available capacity. Entries and exits should be allocated with this goal in mind.

You should also try to ensure that most (if not all) of the movements that could be performed before you add the extra carriageway can still be performed afterwards. If you stop traffic from doing what it could previously you may generate extra congestion elsewhere as traffic redirects, reduce the effectiveness of any services that used the old routes, or even jeopardise deliveries that are essential for your commerce and industry. Replicating movements often requires quite complex layouts, as seen below.

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437535129

Most of the principles for real C/D systems apply in C:S. You can actually learn quite a lot just by looking at them on Google maps and thinking about what each ramp is doing. There are, however, a couple of ways in which real C/D principles don't fully apply in C:S.

In real life C/D systems like the 401 in Ontario, the outer carriageway is usually for local traffic and has lots of entries and exits and the inner carriageway only has entries and exits at major interchanges. If you are building a C/D system from scratch in C:S, that is probably the best way to do it. But if you are upgrading an existing road, there is no reason to follow this rule, and often it would require much larger land take. In my C/D systems (see below), there are a similar number of entries and exits on the inner and outercarriageways.

In real life, C/D systems usually have two carriageways in each direction. There is again little reason to systematically do this in C:S as the game generally generates more congestion in one direction than the other. Hence my examples below all have two carriageways in one direction and only one in the other.

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437542090

Here are three examples from my city:

Example A - two highways get funnelled into this section before the traffic splits at a major four way interchange. The less busy highway is put onto the outercarriageway; as I want to balance flows between the carriageways I also made the outercarriageway the only way to access the left turn at the four way interchange.

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437374845
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437375195

Example B - this is the biggest C/D section in my city. The new carriageway is mostly in the water, as this is the only place where there was room. This means it is on the 'wrong' side of the existing highway, i.e. it is going in the opposite direction to the nearest carriageway.
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437375015
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437375296

Example C - this section between a four way highway interchange and an industrial area was highly congested. The ramps from two of the highways form the outercarriageway, which has several exits in the industrial area.
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437375118
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437375377
Overall map of my highway network (example A is to the NW, example B is to the SW, example C is to the NE): https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=437374762

There is some light congestion on the C/D sections but vastly improved from the long lines of stationary traffic that was there before I put in the extra carriageways :)