Select the object you created and strike the w key to bring up the translation tool.
When you access the tool, a control handle will appear at your object's central pivot point, with three arrows aimed along the X, Y, and Z axes.
To move your object away from the origin, click any one of the arrows and drag the object along that axis. Clicking anywhere on the arrow or shaft will constrain movement to the axis it represents, so if you only want to move your object vertically, simply click anywhere on the vertical arrow and your object will be constrained to vertical movement.
If you'd like to translate the object without constraining motion to a single axis, clicking in the yellow square at the center of the tool to allow free translation. When moving an object on multiple axes, it's often beneficial to switch into one of your orthographic cameras (by clicking spacebar, in case you'd forgotten) for more control.