It is often said preparation is the key to a quality finish. 

A lot of time is spent preparing surfaces prior to painting or papering to ensure a lasting, quality finish. Here are the many stages required for a proper job.

Masking off
Firstly surfaces not to be painted are masked off or covered up with dust sheets
Using a variety of masking tapes with different levels of grip, masking paper, plastic sheeting, self-adhesive films it is possible to ensure the paint only goes where it is supposed to and nowhere else.

Cleaning
Paint has trouble sticking to dirty surfaces. It is essential that surfaces to be painted are free of grease and dirt before work commences. Areas around door handles and at hand height on architraves and door frames are especially prone to adhesion problems.

Sanding
Has two purposes. It provides a smooth surface, removing imperfections. Secondly it promotes adhesion by 'keying' the surface, giving the paint something to stick to.

I use dust extracted sanders to minimise dust and permit more sanding and a finer finish. More details here.

Priming
Any bare surfaces need to be primed. In the case of new plaster a 'mist-coat' of thinned down emulsion is applied first. This soaks into the plaster to create a proper bond, neat paint would not penetrate and just sit on the surface resulting in failure of the paint film sooner or later.

Regarding woodwork, before it can be primed any knots need to be treated otherwise they will bleed through the topcoat regardless of the type of paint used.
White shellac knotting is ideal for this.  Following knotting woodwork is primed and the filled.

Filling
Dents, dings, holes, cracks, splits and shakes are filled with a wide range of products.
From standard powder fillers and jointing compounds for walls and ceilings, two-pack car body type fillers for long lasting woodwork repairs, expanding foam for large voids, caulk for cracks and even lightweight fillers made out of glass beads for small surface imperfections.
Filler is most often applied to primed surfaces to avoid porous surfaces sucking the goodness out of the filler - causing early failure. 
After sanding, fillers are always primed to prevent 'flashing' cause by painting a surface with uneven porosity.

Painting
If all the preparation has been properly taken care of then the painting can seem like the easy bit!
Broad-wall/ceiling surfaces are normally taken care of with rollers, larger rollers up to 15 inches are used on ceilings to speed things along.
9 inch rollers are standard fayre for walls in the domestic environment.
4 inch mini rollers of a medium pile are useful for getting behind radiators, with mohair and foam variants used for evenly applying trim paints which are often then laid off with the tips of a brush.
A HVLP sprayer is sometimes used for spindles on staircases and other intricate surfaces. 
There is such a vast array of paint brushes and rollers on the market, not all are created equal or suitable for achieving a quality finish and it takes years of experience to know which applicators are best to use with each type of paint.