TL;DR: To minimise noise, get as much light as you possibly can through the lens (since noise is mainly caused by low light levels) by using appropriate aperture and shutter speed settings.

Then while keeping these settings constant, increase ISO as far as you can (without clipping highlights) as this will reduce the proportion of the signal that is read noise.

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Is lower ISO always better?

No!

For a fixed amount of light coming into the camera, lowering the ISO will not result in a reduction of noise (improved signal-to-noise ratio). The only way to reduce noise is to combine lowering the ISO with letting in more light by opening the aperture or leaving the shutter open longer.

If the amount of light you can let in is limited (you have hit the max aperture and can't use a longer shutter speed without introducing blur) then using the highest ISO possible (without clipping highlights) will lead to the lowest noise in the image. This is going to seem counter-intuitive and invite downvotes (seven so far!), so please let me explain (see my response to comments at the end).

High ISO values don't cause noise, lack of light causes noise. The reason people associate high ISOs with noise is because when you increase the ISO setting in shutter or aperture priority mode, the camera either closes the aperture or increases the shutter speed to compensate, both of which decrease the amount of light coming into the camera.

Here's an explanation of why low light results in noise:

One important source of noise in images arises from the random nature of light and is called photon noise, or shot noise. Photons are emitted randomly from light sources. If you collect a lot of photons the randomness averages out and you get almost exactly the same number emitted in each direction. If you collect much fewer photons the number collected in neighboring pixels (that should see the same color) can differ giving brightness variations referred to as noise or grain. This is how lack of light leads to noise. See Wikipedia: Shot noise.

Another source of noise is read noise. Read noise happens when the analogue charges on the sensor are digitized (read out). Read noise is approximately constant with respect to the number of photons captured. Increasing ISO amplifies the signal, and thus the photon noise, but the read noise stays the same.

If you use a lower ISO (with the same amount of light coming into your camera) you will get an underexposed image and when you brighten it in post you will amplify both the photon noise and the read noise. Your total noise will then be higher.

Here is an example of this effect in practice:

These images were shot with identical settings bar ISO, and processed in exactly the same way. The bottom one is clearly noisier, despite being shot at ISO 100.

If you were to plot noise vs ISO for every pair of shutter-speed/aperture, you'd find noise always increases (sometimes only slightly) as ISO decreases. Therefore I don't see how you can argue that high ISO results in noisier images, given that when all else is equal lower ISOs give more noise!

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Response to comments

Sorry, but your explanation doesn't change the fact that your basic statement is wrong. What you normally want to use is the lowest ISO that will give proper exposure with a usable combination of shutter speed and aperture

The method you use is of no real consequence, when you think about it using auto-mode and picking the ISO value that results in the shutter/aperture being as long/wide as you can get away with is equivalent to just setting the shutter/aperture to be as long/wide as possible in the first place and then setting the ISO to obtain the correct exposure.

However, I wasn't suggesting a shooting methodology, the point I was making was, to minimize noise, you want to let in as much light as possible, given that you have achieved this with shutter/aperture/flash or whatever, the ISO should be as high as possible (before highlights clip), as anything else will result in underexposure and thus more read noise.

if you actually do change your shutter speed and/or aperture (following the law of reciprocity, as one would normally do), then guess what: you get more photons on the sensor for the same "exposure" (call it EV as adjusted for the ISO in question)! So, less noise!

Yes but you can't increase the ISO and at the same time change settings to let in less light and then conclude you have more noise because you're using a higher ISO. Especially when you can show that if you increase the ISO on it's own you decrease noise!

It's like buying a car with a smaller engine in order to reduce fuel consumption, driving everywhere with your foot flat to the floor and concluding that small engines increase fuel consumption! Change one variable at a time.