I need to join my fence with my neighbor's; Can't use his post..how do I dig the hole for mine close to his?
I would (and have) set your post at least 2' from his. So it would end up looking like this

 -        -
| | -----| |-------------------
| | |    | |                  
| | |    | |                  
| | |    | |                  
|A| | B  |C|          D       
| | |    | |                  
| | |    | |                   
| | |    | |                  
| | -----| |-------------------


A = neighbors post

B = your fence panel cantilevered beyond your post

C = your post

D = your gate/fence...

If you set your post too close to his, then both posts will end up being influenced by the other...as one leans/sinks it will more likely affect the footer of the post immediately next to it.