For a rectangular array you can use the array modifier in the modifiers tab, but for a circular array I choose to use the spin tool, and make duplicates. You can make circular arrays with the array modifier, but you have to use a reference object for this to work well.
For a rectangular array:
- Select object you wish to array
- go to modifiers tab and add an array modifier
- set numbers of copies you wish to make and their offset distances in the direction you wish them to go.
- If you wish to add another array in another direction, create another array modifier for the same object and repeat above.
Modifiers are awesome in that you can change their values at any time, such as number, and offset, as long as you don’t “apply” them.
For radial array I use spin in edit mode.
- select the object you wish to array
- place 3D cursor where you want the action center to be
- set the view to the correct orientation, your view point will create a “plane” in which the action will happen, so if it is supposed to happen on the ground choose a top orthagonal view.
- in the tool shelf, hit spin
- at the bottom of the tool shelf select the number of copies, set it to duplicate and the angle of the duplication.
- after the spin command, remove doubles
I won’t go into the radial array through the modifiers tab here, but if you want to know, just ask.
Of course these are simple approaches are there are more complex possibilities available.