How to move an object in dwarf fortress

To safely release the goblin where you want it.

Build the cage, using build, caje, expand (to show all cages and their contents), and build the cage where you want it.

You can then connect a lever to the cage (query the lever, add a task to connect to the cage, and use that to release the caged creature (goblin or otherwise) by pulling the lever (add a task to Pull).

You can also use the take from stockpile command to move them to another stockpile.

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.