How to dig up, through a level surface?

Dwarf Fortress uses a Wall/Floor system to handle its staircases. That is to say, to connect between two different z-levels, you need a down stairs on the floor of one level, and an upstairs on the wall of the level below that. (An up / down stairs is simply any tile with both an up stair in the wall and a down stair in the floor).

When breaching a surface from below, this means that all you need to do is designate a downwards stairs on the surface tile itself. If there is an up stair on the z-level directly below it, dwarves will be able to access it upwards.

So there are several ways to do this. It depends on whether you want stairs (straight up/down connections) or ramps (diagonal up/down connections), and whether you want to mine the upward path into a "natural wall" tile on the lower level (anywhere not yet mined) or build it into an open space.

If you have a natural wall on the lower level that you're willing to mine into and you want to make stairs:

1. Mine an "up stair" (d-u) or "up/down" (d-i) stair into the lower wall tile.
2. Mine a "down stair" (d-j) or "up/down" stair into the tile directly above that one.

If you have a natural wall tile on the lower level that you're willing to mine into and you want to use a ramp:

1. Mine an "up ramp" (d-r) on on the lower wall tile.
2. Pick a wall tile adjacent to your new ramp on the lower level. If there isn't one, construct one (b-C-w).
3. Mine the tile above the wall you just picked/built, however you like. You can put another up ramp or some stairs there if you plan to keep going up, for example.

If you want to construct stairs in open space:

1. Build "up stairs" (b-C-r) in an empty tile.
2. Mine "down stairs" (d-j) or "up/down stairs) (d-i) into the space immediately above.

If you want to construct a ramp in open space:

1. Build an "up ramp" (b-C-r) in an empty tile.
2. Channel (d-h) the tile directly above the new up ramp. (Your dwarves can reach the upper tile now from the ramp, but unlike with mined up ramps, they won't automatically mine it as part of creating the ramp itself.)
3. Pick a wall tile adjacent to your new ramp on the lower level. If there isn't one, construct one (b-C-w).
4. Mine the tile directly above the wall tile you just chose or built. As for mined ramps, you can put stairs or another ramp there if you want.

Some extra notes:

• See this answer for why you need the adjacent walls when using ramps. Once you're all done, make sure not to mine out those walls later or your ramps will stop working. If you ever do mine them by mistake, just rebuild them with b-C-w to make your ramp usable again.
• To target a tile directly above something, here's an easy way to line it up. Start on the lower level, and press (d-j) or (d-h) as applicable. Then, line your cursor up with the tile you want to be on top of. Next, hit < to go up, and hit enter twice to designate the tile without moving your cursor. It may just look like your designation is floating in empty space if you're mining up into an unexplored level, but if it's positioned as I describe here it will work.

Carve a ramp, they go upwards. You can then build a downward staircase and replace the ramp with an upward staircase. The ramp may become unusable after constructing the upper staircase, so send that fish dissector if the area is dangerous or you are expecting delays.