Pieces of stairs:

Railings:

• Balusters: Spindles or pickets that connect the railing to the ground- square, plain, fluted, twisted or octagonal in a variety of styles.
• Newel post: Main post at top and bottom of stairs and on platforms.

Stairs:

• Treads: The section of the stair that one steps on.
• Risers: The section of the stair that is perpendicular to treads
• Stringers: This section holds the treads and risers together and adds stability.

All parts of the stairs can be finished the same, some parts can be painted while others are stained, the treads can be totally carpeted, or have carpet applied just up the middle runner style so the ends are exposed (tread caps).

Stairs can be made in many different styles, but because what one person thinks of "Colonial" is another person's "Victorian" it's a good idea to actually look at the styles available to make a final choice.