@eDiIeE sub plots are like colored threads you weave together to make cloth. If you only use one color/plot, your story could turn out boring. The more colors/plots you use, the richer a feel you'll weave.
Harry Potter has a lot of plot lines (Harry vs Voldemort; Order of the Phoenix, the various romances are each a minor plot line; and so on). One reason the Harry Potter books feel so full and rich is all those plot lines woven together.
Keep in mind, though, that even JK Rowling started out writing one-plot stories. Even the first Harry Potter book is not so full of plot lines as the following books. And just like someone who knows the basics of weaving cloth can't sit down and weave a tapestry without practicing the basics for years, so an inexperienced writer can't sit down and write a story with loads of expertly woven plot lines.
Now for how you do this. To start, try outlining a plot for each "part" you have in mind. Figure out the plot for Part A and then do the same for Part B. You'll want the beginning and ending for each part and then a couple of exciting points in between. And once you do that for both parts, you can figure out where the plot lines intersect, that is, where the people in Part A meet or deal with the people in Part B.
Your simple outline will look something like this:
PART A
Beginning:
Meets Part B:
Middle: If you start on an adventure, this point is where you are halfway there.
Ending:
PART B
Beginning:
Meets Part A:
Middle: If you start hating that guy who will end up your best friend, right around here you decide he might not be so bad.
Ending:
