The parenthesis in the top-right corner of the Dwarf Fortress window

to be functional, a stairway needs stairs in both levels (above and below), here's an example:

level 0:     level -1:          legend:
.....        .....              . floor
..>..        ..<..              > down stairway
.....        .....              < up stairway

You can create stairways with two methods: either through mining (d) or through the construction menu (b C). Use the mining menu when there is rock or soil at the location of the future stairway. Use the construction menu when there is nothing at the target location.

If you have already mined out a level and you need to access the floor above, you'll need to create an up stairway (b C u). If there is a natural floor above you will need to mine it out (d j) to have both parts of the stairway.

If there is no floor above (the tile has been channeled or maybe you're building a tower), construct a down stairway (b C d) on the level above your up stairway.

See the example of the construction of a tower on magmawiki for further reading.

On the left side, the colored letters near the top note if there are reports that you haven't looked at. Different letters stand for different reports (source). C is combat, H is hunting, S is sparring (military).

On the right side:

• The bottom number shows your current depth on the z-axis, as you mentioned.
• The coloration along this bar shows the dominant features of nearby levels (with the current z-level being in the center, highlighted yellow. Blue on this bar indicates empty space. Brown indicates earth and stone.
• The number in the top right shows your current z-distance from "center." If you are below the "center" level, it will show red. If you are above, it will show green.

The top bar shows if you are paused and the current number of idlers (dwarfs without a task to do). In older versions, the idlers will instead be on the bottom.