From within the Awards manager, there is a link to export what you see on screen to Excel. Use the filters to find the award records, then select the ones that you want to export either by checkbox or by right-clicking and Select then All. Selecting the Export to Excel link on the left navigation bar will prompt you for a filename and where to save the file, and then will produce an Excel file of the records you selected.
For more flexibility, use the Advanced exporter: select a Data source of Awards then set your filters. This lets you export not only properties of the awards but also extensive data about the volunteers who were nominated for each.