I am developing a C# program by using Aster.Net library. The objective of this program is to display the Caller ID once the agent picks up the call. Can I know which event do I need to monitor?
Hi,
Assuming you’re using AMI…
Use the AgentConnect event in ManagerConnection. Once this event is raised,you can access the CallerIDNum and CallerIDName properties. Off the top of my head, not sure if you need to look at ConnectedLineNum and ConnectedLineName also. Pop a break point in there and have a look! 
AMI is good method, also you can use Queue GoSub() and another method is set the option
setinterfacevaretinterfacevar= yes, If set to yes, the following channel variables will be set just prior to connecting the caller with the queue member:
MEMBERINTERFACE: the member’s interface, such as Agent/1234
MEMBERNAME: the name of the member
MEMBERCALLS: the number of calls the interface has taken
MEMBERLASTCALL: the last time the member took a call
MEMBERPENALTY: the penalty value of the member
MEMBERDYNAMIC: indicates whether the member was dynamically added to the queue or not
MEMBERREALTIME: indicates whether the member is included from real time or not
Look this: https://wiki.asterisk.org/wiki/display/AST/Pre-Dial+Handlers and https://wiki.asterisk.org/wiki/display/AST/Pre-Bridge+Handlers
Using AsterNet: https://asternet.codeplex.com/wikipage?title=Handling%20Events&referringTitle=Documentation
Forgotten I’d even written that! Should really move that content over to GitHub!