How is an action potential conducted across axonal branches in a neuron? As the action potential travels in the dendrite towards the cell body, it may encounter axonal branches. What happens at the branch? What makes it go to the cell body instead of other dendrite?  

Also, as the action potential travel from the axon to its branches, does it go to only one or all terminals? If it goes to only one terminal, how is it decided which terminal it has to go?
Often action potentials arise not until the initial segment of the axon, sometimes referred to as the   axon hillock. This has to do with a critical density of voltage-gated sodium channels needed for action potential generation (Kole et al., 2008). The way it is conducted though the dendrites is hence often by means of graded dendritic potentials.

Axon terminals are not "gated". The axon potential simply is conducted through all of them (see e.g., Anesthesia Key), barred any refractory effects or inhibitory or excitatory inputs from axoaxonal connections.

Reference
- Kole et al., Nature Neurosci (2008); 11: 178-86