IMPORTANT: "Gallons," "gals," and "gpm" refer to the US Imperial Gallon , as opposed to the UK Imperial Gallon.
Try and find a place in the stream where it drops quickly over a rock, place your bucket below and measure the time to fill it.
At lower flow rates, less than 150 gpm (10 l/s) you need to be accurate in measuring the flow. If you have a 2 gallon paint pail and the river can fill it in 2 seconds you have 1 gps = 60 gpm, this equates to 227 l/min, 3.79 l/s.
Use the largest possible bucket you can find as the longer it takes to fill the more accurate your reading will be.
For flows greater than 150gpm try to estimate your flow using a larger bucket in the river and measure at various places across the river. It will not be as accurate but at higher flows it is not that critical.