Upon opening Blender, you may notice that the default cube has a orange outline around it; this means it's selected. If you're new to Blender but are familiar to another program, the first thing you might try is to select either the light or camera also present in the default scene. And if you did indeed use the LMB to try to select another object, you'll notice that it didn't result in a selection. Instead it moved the red and white circle with black lines around the scene. This is the 3D Cursor, and by default you use the LMB to reposition it (Figure 1).
In Blender, by default, you use RMB to select objects. Try now selecting the camera with the RMB, then the light. Each object that is selected assumes the orange outline.
If you want to select more than one object at a time, hold the Shift key down in conjunction with RMB. Note that all objects have an orange outline, but the last object selected has the lightest shade of orange for its outline (Figure 2). The last object selected is also known as the Active Object. This isn't always the easiest to see, so if you go to your Outliner, notice that the active object is also the object with its name highlighted in white.
To deselect an object, also hold Shift + RMB.
Hit the "A" key. Notice that all objects are deselected. Hit "A" again and notice that all objecst are now selected. "A" toggles between selecting all and deselecting all. This works for more than just objects.
You may also make an inverse selection with CTRL + I after selecting objects you don't want selected.
Deselect all again with the "A" key. This time hit the "B" key. Crosshairs will appear on screen, waiting for you to LMB-drag a selection. This is the Border Select tool, and it works just like marquee-selecting. Go ahead and use this tool to select multiple objects in your scene to see how it works. After you let up with LMB, the cross-hairs disappear. If you want to make another border selection, you have to hit "B" each time. If you don't hit "B" first before LMB-dragging in the screen, you may get strange results (like moving the selected object).
Another option is to "Circle" select using "C." You can think of this as "brush selecting." However, this method is more suited to Edit Mode, as if used in Object Mode, you must click on the object centers to actually select the objects. Like the Border select tool, use the LMB to make selections while in this mode. Hit <Escape> or RMB to end the Circle select tool.
All these methods are also available through the "Select" menu at the bottom of any 3D view.
If you don't like the way Blender RMB-selects objects by default, you may change this. Open a User Preferences window. (Figure 3).
Select the Input button to change to that section (the button will turn blue when selected). Find the "Select With:" section at the left and click on "Left" to activate LMB selecting (Figure 4).
Now, you will use LMB to select and RMB to reposition the 3D Cursor... test it out! Just realize that if you do this, some functionality will be switched. All the tutorials on this site will be based on RMB-selections, as well as several other tutorial sites out there.
To keep this functionality next time you open Blender, you must "Save User Settings" by hitting CTRL + U (or Save As Default button in User Preferences window). Keep in mind that this saves what view you're in also. In other words, if you do this while in the User Preferences window, the next time you open Blender, you will see this window rather than the 3D view. So, you might want to configure some other things like split views, etc. and then Save User Settings.