I've long ago discovered how to access control properties and methods from other controls, but never needed to access those properties and methods from a component class.
Say I'm in a control and need to call a method of another control:
C_CntrlClass uc_cntrlid = (C_CntrlClass) Page.FindControl("uc_cntrlid");
uc_cntrlid.Method(param);
But what about calling that same Method from a class component? Since the class does not inherit the Web.UI.Page class, it does not expose the Page object. This is where the IHttpHandler object comes in:
System.Web.UI.Page pg = (System.Web.UI.Page) System.Web.HttpContext.Current.Handler;
C_CntrlClass uc_cntrlid = (C_CntrlClass) pg.FindControl("uc_cntrlid");
uc_cntrlid.Method(param);
From the MS-HELP IHttpHandler documentation: "HTTP handlers give you a means of interacting with the low-level request and response services of the IIS Web server and provide functionality much like ISAPI extensions but with a simpler programming model."
Here's the google thread which pointing me in the right direction, with special thanks to Kevin Spencer's comments.