Zoom into an area of interest. Open the Hydrometric folder under Map Layers and turn on the layer "Active Hydrometric Stations" (you have to be zoomed in to some degree, more than 1:500000 or so). Click the "i" icon next to the checkbox for the Active Hydrometric Stations layer (this allows the identify tool to be used). Pan and zoom as needed, turn on other layers if useful.
Click the identify tool icon at the top of the map (an "i" in a black circle). Then click on a hydrometric station dot. The results should appear on the right side where the map layers were. Make a note of the station number.
Under the Identify Results click the Archive_Url "More data" link. This opens the Archived Hydrometric Data search page. Seems like it ought to take you to the station in question, but it doesn't seem to. So type the station number into the search box and click Next.
An Archived hydrometric Data page should come up. It should list just one station, the one you entered. If more come up, select the one you want first. Note the station list includes the station's full name, its coordinates, and drainage area it measures (useful for watershed size if the station is near the mouth). Also note the data years (eg, 1960-2008). Some stations have very limited years, others are discontinued, which might result in poor stats.
To get long-term mean annual discharge, select "Monthly Data" in the "Report Data Type" menu, then click "Obtain Report". A table should come up listing discharge numbers by year and month, with a mean column for each year. Scroll to the bottom. After the last year listed there should be a Mean row. The number in the Mean row's Mean column is the mean annual discharge for the station's total life. Max and min numbers are also given. They are monthly mean max and min rather than daily max and min, so may or may not be desired.
To get daily mean max and min, go back a page to the station list and select "Peak" instead of "Monthly Data". Click "Obtain Report". The page that comes up shows the max and min daily discharge per year. It looks like you have to figure out the overall max and min numbers for yourself.
Once done, you can go back two pages to the station search page and enter another station number and do it all over again.
I'm not sure how best to source this info in a citation.