Introduction to ArcGIS

Three main modules: ArcCatalog, ArcMap and ArcTools

ArcCatalog

Moving, deleting, copying spatial datafiles
View, create, edit metadata
Search for data

ArcMap

Visualization, cartography (and analysis…)
Vector data editing (ArcEditor)
Some analytical functionality

"GeoProcessing Wizard" - vector data manipulation
Spatial Analyst - raster data manipulation
Data conversion tools

ArcToolbox (now a module/dockable window within ArcMap)

Analysis, manipulation - mostly (legacy) tools for manipulating shapefiles and coverages, for working with Geodatabases most tools exist in ArcMap

Data conversion tools (first place to look for import/export tools)

ArcInfo Workstation

Old command line functionality
AML - Arc Macro Language

A note on the evolution of ArcGIS

Database engine for native vector format in ArcGIS (Geodatabase) is now MS Access
Programming interface for ArcGIS is now Visual Basic and Python (formerly Avenue and AML)
Major development platform for ArcGIS is now Windows (formerly prime/VAX, then Unix)
Handheld applications built using Windows Mobile

Getting Help

ArcGIS has a decent help system, I strongly encourage you to become familiar with it as learning how to navigate the help system is a critical step in independent problem solving. Accessible through all modules (just see 'Help' button on main menu line).

ArcGIS also has contextual help, if you click the "What's this?" icon (arrow with question mark on main menu) and then click on some item in the ArcMap window or dialog box, you will often be presented with helpful information that tells you about those elements.

Another tremendous resource is the support pages at the ESRI website. There you will see both technical documents published by ESRI staff as well as discussion forums users use to solicit and provide help from the user community. Both the technical documents and forums have a trove of answers to a wide array of technical questions. Both keyword and application searchable.