If you are fortunate to have a stream on your property, then you certainly want to be able to access the water for use in your garden. Of course, you can always use a bucket, but that would be tedious and slow. Instead, you can use a pump to raise the water out of the stream and across your yard to the garden. There are a few details involved, as usual.
Purchase a pump for your irrigation system. Typically, a centrifugal pump is used for this setting. Determine how high you want to raise the water, and measure the distance from the water to the top of the bank. If your garden is still higher, then add that measurement in to get the total. You will also want to know how many gallons per minute you are expecting. A typical garden hose puts out anywhere from 10 to 23 gallons per minute, if you need a reference.
Set up the plumbing for your pump. Consider hiring a plumber at this point to make sure all of your connections are waterproof. The fittings to your pump may be a different size than your hose size, and you may have to get some adapters. Place a foot valve on the end of the hose that goes into the water so that the water doesn't drain out of the pump when it is off. It will also prevent debris from being sucked up into the pump.
Prime the pump after you plug it in by filling the section of hose that goes into the water with water and then turning on the pump. You will hear the change in sound as it goes from pumping air to pumping just water. Make sure the garden end of the hose is left open.
Water the garden directly with the pumped water, or store it in a water/rain barrel that can be accessed later for watering on demand.