In the Reports Tab, you can find the report by changing the View Folders Options, Searching in the folders below, using a keyword search, of it it something that you have worked on recently, it will appear in the recent reports tab.  Use the hyperlink of the report name to open that report.

Make sure you have the right options, views, and time frames set to gather the correct information for your report.  

You will notice in this report that we are  getting all contacts created for this year and the last 2 years.  This produces 51,536 records, which we won't be able to view in Salesforce. So we'll want to export this data.

In this example, I am summarizing by organization, and I have hidden the detail.  

Notice however, hat that export Details button still says "Detail".  

The export function only exports details, and does not export your summaries or groupings.  You can regroup in excel after the data has been exported.

Click the Export Button, and a new window appears.

Always choose the ISO-8859-1 (General US & Western Europe...etc) as the Export File Encoding.   This is the most commonly used coding.  If, however, your analytic software needs another coding, this is where you choose that option.

Generally, we use the file format CSV.  This is so that it will work with the APEX Data Loader, and other software programs.  If, however, you are only using Excel, you can choose that here, as well.

When you hit Export, a screen will pop up asking you where to save this file.

If you already have all the settings you require and you just quickly want to export a file, you can do so from the Main Reports window by clicking on the Export link next to the name of the report you want to work on.  This will take you right to the export report window.