This is a frequently asked question from a novice. If you have come from ASP.NET background or worked with Web Application development then learning server is fairly easy. You will need to start learning Java language, Java Servlets, Java Server Pages, and then Java Server Faces. If you are familiar with .NET languages (VB.NET/C#) then OReilly’s Java in a Nutshell will be of good use or go for Core Java series for complete reference.
I strongly suggest you go through ‘Java EE 5 from Novice to Professional’ from Apress publications , ‘Core Servlets and JavaServer Pages’: Volume 1: Core Technologies, 2nd Edition, from Prentice Hall PTR. These books gives you overall understanding for enterprise applications, JSPs and Servlets.
Once you brush up the above topics, delve into ArcGIS Server. First and foremost thing is study “ArcGIS Server Administrator and Developer Guide’ from ESRI. This books gives you complete understanding for Server concepts. Developer guide chapters will be useful once you have good idea on java/jsp. Developer Help is much important document one has to go through. This is comprehensive guide for server based GIS.
Start learning with ESRI samples and understand them. Then start developing your applications. ESRI Forums, EDN, ESRI Blogs will be handy. Download some PPT’s from ArcScript section presented in ESRI developer summit/UC’s.
http://java.sun.com/javaee/5/docs/tutorial/doc/ (part II web Tier)
ArcGIS Server docs can be found here.