Blender's viewport is a dynamic, changeable interface composed of many different windows. With the program running by default, the viewport is composed of 5 different windows. Windows can be identified by looking for their small square indicator icons either in the top or bottom-left corner. They may look like these:
These small images denote the type of window they're attached to, and the window type can be changed by clicking on one of them and choosing another window.
All of the windows are resizable and splittable, meaning that they can each be split into two pieces, changed in size, or be combined together into one window.
To try this functionality, first take note of the location of the screen layout selector which appears at the very top of the screen just after the menu buttons:
This selector will let you get back to the default window layout at any time, and acts (like many of Blender's selectors) as a dynamic list. This means that if you'd like to save this layout before you start experimenting, click the + button to copy the layout, and then make your changes. Return to the layout by clicking the layout name and selecting the default again.
Now that the layout can be returned to, drag one of the grab handles at the corner of the main window - it looks like this:
Your cursor will transform into a crosshair and the window will split in half.
Combining two windows together can be done with the grab handle from the opposite corner of the window. In the image above, the grab handle used to split the window was in the bottom-left corner: thus the grab handle used to combine the window with another is the one in the top-right.
To combine the window with another, just drag this second grab handle in the direction you want to combine. You may have to pull it away from itself first, if you want to collapse it inwards, like so: