It's possible to add several modifiers to the same object at the same time. in that case the modifiers are applied in the same order that they are stacked in in the modifier panel, starting with the one at the top. Therefore there are buttons that allow you to change the stacking order.

We will examine only the most useful modifiers such as Mirror and Subdivision Surface (also called 'subsurf'). Modifiers apply to one object at a time, so if you turn on the mirror modifier for one object in a scene, for example, it will not affect any other objects.

Mirror Modifier

Many modelling tasks involve creating objects that are symmetrical. Using the mirror modifier means you only have to create one half of the model and the other half will be created automatically, saving you a great deal of time.

The Mirror modifier automatically mirrors a mesh along its local X, Y and/or Z axes, which pass through the object’s centre. We will examine only mirroring along the X axis, which means mirroring about a YZ (vertical) plane. Here is half of Suzanne's head and its mirror image, mirrored along the X axis. A gap has been left between the two halves to emphasise the mirror process, but normally there would be no gap.

To use the mirror modifier on a selected object, open the modifiers panel and click the 'Add Modifier' button then choose 'mirror'. The following panel will open:

You must be in Edit mode to use the mirror modifier. The mirror modifier can be set to join vertices to their mirror images if they are within a specified 'tolerance distance' (the 'merge limit') of the mirror plane. This is called 'clipping' and is recommended because

If you want to separate vertices that have been clipped together then you must first turn off the clipping option.

Try it yourself

To experiment with the mirror modifier, start a new project, delete the default cube, add the monkey mesh and rotate the monkey mesh so that it is facing the front. One way to accomplish the rotation would be to use the 3D rotation manipulator with the Ctrl key held down while watching the lower left of the 3D window until the angle is shown to be 90°.

Switch to Edit mode and unselect everything (A). Then switch to front ortho view and vertex select mode . We are about to box select the vertices left of the centre line but box select won't select surfaces that are hidden round the back so be sure that the 'limit selection to visible' option is turned off (unselected) before you do the box select. Now use box select (B) to carefully select all vertices left of the centre line.  Delete these vertices and you should see half of Suzanne's head like this:

Note that the object centre (the orange dot) is correctly placed on the plane that we are about to mirror about. It's a good idea to keep the 'real' surfaces on one side of the mirror and the mirror images on the other. Blender allows you to have real surfaces on both sides but that's a bad idea. Now add the mirror modifier as described above, with clipping turned on, and try moving vertices, edges or faces. See what happens if you move a vertex to the mirror plane - note how the vertex is clipped to its mirror image. Try selecting vertices, edges or faces on the 'mirrored' side - you will find it is impossible.

If you want to do anything to this object that would make it unsymmetrical then you will first need to click the 'Apply' button - the modifier will be applied and will then close. But if you do not need to make the object asymmetric there is no particular need to 'apply' the modifier - images can be rendered normally even if the modifier has not been 'applied'.

For a fuller description of the mirror modifier, see

wiki.blender.org/index.php/Doc:Manual/Modifiers/Mesh/Mirror

Two other types of mirror (not modifiers)

Do not confuse the mirror modifier with the mirroring (Ctrl+M in Object mode) that simply 'flips' the selected object. Do not confuse the mirror modifier either with the 'X mirror' option in the tool box. If you have an object that is already symmetrical along the X axis and you want to modify it while keeping the symmetry then do not use the mirror modifier, otherwise you will have to carefully delete half the model first. Instead, while in Edit mode for the object, turn on the 'X mirror' mesh option in the tool box: .

To experiment with this, add the Monkey mesh (a.k.a. 'Suzanne') to an empty project, rotate her vertical using the 3D rotation manipulator with the control key held down so as to constrain the rotation to 5° increments (watch the rotation angle at the bottom left of the 3D window until the angle is 90°). Then switch to Edit mode, turn on the X mirror option, select a vertex, edge or face and try moving it.

Subdivision Surface Modifier

The smooth option in the tool shelf adjusts the colours on each face to hide the edges between faces - it does not increase the number of faces and this it not capable of really smoothing the shape.

To increase the number of faces and get a smoother shape we can use the subdivision surface modifier (also called subsurf). Not only does the subsurf modifier give you a smoother shape but it has another great feature too – it lets you remove the additional faces at a much later time if you want to, or add even more faces if you choose. This is much better than the usual ‘undo’ option (Ctrl Z) which can only be done immediately after you make a mistake. This ‘anytime undo’ feature comes at a price – there are certain operations that you can’t do on these new faces, such as ???????? If you need to do such operation then you will have to ‘APPLY’ the subsurf modifier, which makes the new surface into standard surfaces just like any other. Once the sursurf modifier has been ‘applied’ you cannot adjust the modifier so as to reduce or increase the number of faces because the modifier panel closes once the modifier has been applied. However you still have the UNDO option, Ctrl Z, to un-apply the modifier, or ‘bring the modifier back to life’, but you will have to undo every step that you did since 'applying' the modifier.

When you open the Modifiers panel and add a Subsurf modifier you will notice that you have the possibility of setting the number of levels of subsurf divisions, both for viewing and for rendering:

The higher the level the more surfaces there will be and thus the smoother the model. Why not set the levels very high then? Because the more surfaces there are the slower your computer will become for it will have to do many more calculations. 'Viewing' refers to your work within Blender and Rendering refers to the final rendering operation - you normally would set the Viewing subsurf level to a number lower than the rendering level for you want your work in Blender to be quick whereas when making the final render the emphasis is on quality rather than speed. Start with viewing subsurf level 2 and render subsurf level 3.