This is not an easy thing to do but will go a long way for keeping you systems more secure. Almost all major network vendors have Web Sites where all of the security patches for their products are at. Visit these regularly to see what is new. Subscribing to the Computer Emergency Response Team mailing list is also a good idea. Read each of the advisories that you receive and see what its affect on your systems is and take appropriate action.
Security is defined by policy.
Policies with security in mind need to be set and communicated to users, administrators and managers. The role of policy is to guide users in knowing what is allowed, and to guide administrators and managers in making choices about system configuration and use. How should the organization react to security incidents and problems. How should the policy itself be updated. Create your policy document and communicate to everyone who needs to know about it.