Panels generally appear in the Buttons window (by default at the bottom, see Buttons window). This window includes a header and many panels.
Each button on the Buttons header groups panels together into what is called a context. And those contexts are grouped further into sub-contexts. For example, all material-related panels are grouped under the Shading context, Material sub-context.
Panels can be aligned by RMB clicking on the Buttons window and choosing the desired layout from the menu which appears (see Buttons window menu). Using Wheel scrolls the panels in their aligned direction, and CtrlWheel or CtrlMMB zooms the panels in and out. Single panels can be collapsed/expanded by LMB clicking the triangle on the left side of their header, to gain space.
Several panels can be grouped together – they then appear as a single panel with tabs (Panel with tabs example). Clicking LMB on a tab in the super-panel header shows this panel’s controls. You can separate a panel from such group by clicking LMB on its tab, and dragging it out. Similarly, you can add a panel to a super-panel by clicking LMB its header and dragging it over the wanted panel (the border of this panel will turn white to indicate that the dragged one will be added to it).
For further details about each panel see their reference section.
Here is a small illustration of panel manipulation.
Starting from the texture mapping group of Material panels, drag out the center tab (Map Input). As you can see, it immediately turns as a whole panel of its own, but with a darker border.
Once you release the lmb button, the dragged panel “flies” to the nearest available position.
Now, you can drag out the Map To panel too, effectively “destroying” the panel group. Note also how Blender “pushes away” existing panels to make room for the one you are dragging – this empty space materializes where your dragged panel will go once released.
However, you’ll rather recreate a new panel group, by dragging the Map To panel over the Map Input one, until this one’s border turns white. This indicates that they will be regrouped together in a single “super-panel”, each one becoming a tab.
Et voilà! Now, you have on one hand a single, standard Texture panel, and on the other hand, a super-panel with two Map Input and Map To tabs. Note that it seems you cannot choose the arrangement of the tabs inside a group, they always take the same order…
Finally, you can collapse the Map Input/Map To group by clicking on its small header’s arrow…