Detonator
A detonator is a tool used to select and remotely detonate various bombs and explosives. There are 4 different types of detonators that can accomplish this task.
Detonator

The standard, gray-colored detonator is used to detonate a single explosive bound by its coordinates. To do so, the player must first crouch and right click an explosive while holding the detonator, selecting and binding its coordinates to the tool; this is now visible while hovering over the detonator in the inventory. Once a safe distance away, the player may remotely trigger the explosive by right clicking the detonator.
If the stored coordinates of an explosive bound to the detonator are incorrect, an error will occur while attempting to detonate the device. No error will result when selecting an invalid coordinate. At any time - before or after detonating - a new position can be designated by crouching and right clicking another block or explosive to replace the currently stored coordinate.
Crafting:
The standard detonator can be crafted in a crafting table using the following recipe:

Multi Detonator

A multi-detonator (red) can be used to detonate multiple coordinate-linked explosives simultaneously. By crouching and right-clicking one or more explosives, their coordinates are added to a list which is visible when hovering over the detonator in the inventory. When the detonator is right clicked, all the explosives at the detonator's stored coordinate list will attempt to detonate simultaneously (invalid coordinates will not stop the detonation of further valid coordinates). To clear the list of stored coordinates, the player can crouch and right-click the multi-detonator in the air.
Crafting:
The multi-detonator can be crafted in a crafting table using the following recipe:

Laser Detonator

The laser detonator is used to detonate explosives from a distance without manually designating its coordinates. To do so, the player must aim the laser at a suitable bomb or explosive using the crosshairs, then right click the laser detonator to attempt detonation. Attempting to detonate an invalid explosive item will yield an error.
Crafting:
The laser detonator can be crafted in a crafting table using the following recipe. Note that either an emerald or diamond can be used in slot 3:

Dead Man's Detonator

A Dead Man's Detonator detonates its single, coordinate-linked explosive, when dropped. The explosive's coordinate pair can be set by crouching and right-clicking the desired explosive. When the detonator is dropped, either intentionally or upon the player's death, its valid linked explosive at the stored coordinates will detonate. Unlike other detonators, this item is single-use and consumed upon activation (it's linked explosive's coordinate pair, however, can be changed multiple times before detonation).
Crafting:
The dead man's detonator can be crafted in a crafting table using the following recipe:

Notes
- All detonators besides the laser detonator store only coordinate pairs, not a specific explosive or 'bomb' itself. When detonating, it will trigger any explosive located at that stored coordinate pair, as long as it is compatible. Stored coordinates in detonators persist even after detonation.
- All detonators must be linked to and trigger the center block of the explosive/bomb. This is important if the explosive has textures that span multiple blocks, such as in the case of Ivy Mike or Little Boy. (Hint: the center block is the only block in large bomb models that can open its GUI).
- Most bombs and explosives may also be remotely detonated with a redstone signal instead of a detonator.