Like it or not, ESRI's ArcGIS family of products is the most common and widely used GIS software. ESRI is sort of the Microsoft of the GIS world. A host of arguably better commercial and open-source free alternatives exist (see here for examples), but as this is the industry standard this is usually what we teach. Below are some useful links to tutorials, forums, manuals and sources of help to get you started:
The ESRI website has a wealth of information on it and provides forums, technical ariticles and a comprehensive online help manual to help you learn how to undertake anything from the most simple GIS tasks to very complicated GIS modelling workflows.
From UNBC GIS Lab: You can download all the ArcGIS Manuals and Tutorials here as PDFs!
If you are not quite comfortable diving right into specifics below (i.e. have never even turned on ArcGIS), this tutorial might be a good place for you to start. The tutorial was developed at the University of Arkansas Libraries and was designed for ArcGIS Desktop version 9.2. The tutorial is intended to help the user bring in their own spatial data of interest and manipulate it in a variety of ways (without having to go through all of ESRI's own tutorials). There are six sections that describe some of the common operations a user may need to know in order to manipulate and/or analyze their spatial datasets:
These tutorials are more comprehensive then the 'Crash Course' tutorials above and are extremely useful (they also include sample data). If you want a more in-depth explanation, spend some time working through these tutorials.
If you want to make a map or a figure, but have little experience using ArcGIS you should have a look at this help file and the links below. Making maps in ArcGIS is done in the ArcMap module using Map Documents.
Whether you have a scanned aerial photo, a scanned paper
map or just a digital map or aerial photo that has no spatial data attached
to it, to use these images in a GIS you need to first georeference them.
tutorial walks you through all the basic steps of how to do this.
To start, you need some GIS layers that are correctly georefereced (e.g.
a base map) and have features you can see in your scanned image or map,
and the scanned map.
The above tutorials all discuss how to bring data into ArcGIS, display it, querry it and potentially modify it. But how do you make your own layers? For example, if you want to classify a landscape mannually by dividing it into regions that you define with polygons, how would you do it? These links provide some of the tools to do this.
A number students have asked me about using GIS to do hazard mapping, land use mapping, soil erosion mapping and simple modelling. You might find the following website useful as it provides examples of a number of these topics and walks you through what the rough methodology is. This website is pushing its own GIS software (ILWIS) but you can do these sorts of analyses in most GIS packages (including ArcGIS, which is available to all of you on any University machine). The nice thing about their applications is they walk you through the basic theory, approximate methods and provide references for more detail. See what you think.