"The first job of a sub-plot is to add a dimension to the story which the main plot lacks. Because fiction is a tidied-up version of life, it is easy to stray into a simplistic portrayal of events which does justice neither to the complexity of real life nor to the intelligence of your readers."
- Nigel Watts
Adding subplots to a novel is all about taking the main plot and adding dimension and complexity to it. I am going to skip the introduction of a subplot for the purpose of delving deeper into how to construct them, but if you need to brush up on the basics go here.
One mistake people often make is thinking that subplots are actually a part of the main plot—just seen through different eyes. But they aren’t. A plot, remember, is about a character pursuing a goal, encountering conflict and reaching a resolution. And a subplot is the same, created in a similar way—introducing the character in their ordinary world, something happens to disrupt the present circumstances, and so on.
The key to not becoming miserably confused when plotting a novel with several plot lines running through it is to treat each plot - the main plot and all the subplots - as entirely separate mini-novels. Begin by working out the main plot, then put it to the side and repeat the process for each of the smaller storylines. There will be a large amount of common ground between the plots, but focusing on each one as a separate story and ignoring the others - at least initially - will result in a much stronger novel.
Once you have your plotlines sketched out, return to the main plot and roughly divide it into chapters (a chapter usually ends at the resolution of a scene). You could do this with paper and scissors and lay out the chapters on the floor, in a long column, or do it on the word processor. Do the same with your first subplot. Then it is simply a process of inserting these chapters into the body of the main plot. Some of the subplot chapters will slip into the gaps in between the main plot's chapters. Others will sit side-by-side with a chapter from the main plot.
Repeat this step with the other subplots. There will be a lot of switching around and merging and altering here, but you should end up with a master plot containing the main plot and subplots. For a while, a particular strand will be at the forefront. Then it will loop out of sight again to be replaced by a different strand.
In some novels, telling the main plot apart from any secondary plots isn't always easy - they can seem equally important. Beware, though, of any secondary storylines overwhelming the main plot. They are there to enhance and strengthen the main story, not to compete with it. The main plot should always begin and end the novel, and any minor plots should happen within these "bookends".
The important thing is this: although the strands are all interweaved (kind of like a braid), they actually remain separate. In other words, it should always be possible to remove an individual storyline from a novel without the story as a whole collapsing. It might weaken it, just as removing a strand from a rope would cause it to lose strength, but the story should still make sense.
The advantage of subplots is that they keep the readers reading. However well you construct a plot, there will always be slower parts punctuating the exciting parts. Slow parts in a story are useful to an extent, in that they help to regulate the pace. But if a slow part threatens to become dull, you can always let the events play out in the background, and switch to an exciting minor plot line instead.