I don't think the USGS site has a way for you to overlay multiple years on a single graph. But you can download the data for each year as a TSV file from the USGS (they call it RDB format), and then import that data into Excel. Once it's in there, you can graph it. The process is a little tedious and time-consuming so if you're going to do more than a few gauges, you may want to automate it somehow.
The other, much easier option, is to use Dreamflows - if they have the gauges you're looking for. Once you click through to the graph on their site, most gauges have a graph that shows the previous 3 years on a single graph. Here's the link to the Dreamflows page for Washington:
http://dreamflows.com/flows.php?page=prod&zone=panw&form=norm&mark=All#Washington_Rivers For example, here's their graph of Ernies for the past 3 years:
http://www.dreamflows.com/graphs/yir.280.php If you want/need the USGS data, here's an overview of the process:
Since you're looking for yearly data, it's probably better to download daily values instead of 15-minute values. For example, here's the USGS page for daily values for Ernies:
http://nwis.waterdata.usgs.gov/nwis/dv?cb_00060=on&format=gif_default&period=&begin_date=2013-12-01&end_date=2013-12-17&site_no=12142000&referred_module=sw If you select only discharge data for this year (2013) and select "tab-separated", you get this page:
http://nwis.waterdata.usgs.gov/nwis/dv?cb_00060=on&format=rdb&period=&begin_date=2013-01-01&end_date=2013-12-17&site_no=12142000&referred_module=sw You can save that page as a text file (.txt) and then use Excel's Data Import from Text feature to pull it into a spreadsheet. There's a wizard that walks you through the import so you can see what you're going to get before you actually import it. But the only 2 columns you probably need are the datetime and the flow.
Then repeat for each year you want, and add the levels for each year as a new column (with the rows/dates matched). Once you've got all the years you want, chart all the data with the days as the x-axis and the flows for each year as separate colors on the y-axis.
If you go the USGS/Excel route, post whatever charts you come up with!