how can i connect internet in my vmware workstation with redhat 5.5

Hello and welcome to LQ, hope you like it here.

Your question is hard to answer because it is missing information like
- what "side" you're talking about (virtualization host or guest),
- how VMware was configured to share or hand off network connections (private subnet, bridged mode, etc, etc),
- the systems network device configuration,
- what steps you took to establish a network connection,
- what (error?) messages you got or what's logged in /var/log/{messages,secure}.

Please reply as verbose as possible: the more nfo the better.