How do cellular processes receive ATP? I know ATP is produced through cellular respiration, but when?

ADP is phosphorylated to ATP along the Electron Transport Chain (ETC), which is a series of metabolic enzymes all lined up next to each other along the inner membrane of the mitochondria.  NADH and FADH accumulate within the matrix of the mitochondria as a result of the Krebs cycle, and these proton carriers donate their H+ ions and pump them across an enzyme known as NADH Dehydrogenase (the first component of the ETC).  This creates an electrochemical H+ gradient that powers an enzyme at the end of the ETC known as ATP synthase, which takes the energy created by the gradient and uses it to phosphorylate an ADP into an ATP.  

The ATP is produced en mass...  ALL the time.  After ATP is produced in the mitochondria, it is exported out of the organelle through transport enzymes into the cytosol of the cell.  It is here that the ATP can be utilized to power cellular processes.  When the phosphate bond is broken on an ATP, it is turned into an ADP.  The ADP then diffuses into a mitochondria and the process starts all over again.  

There isn't an enzyme that really needs to carry the ADP or ATP to where it needs to go.  There is A LOT of this stuff in the cell, and cellular components diffuse and move about quite rapidly.  It gets to where it needs to go on its own.