If there's one supplement I have researched to death, and have lots of experience with, it's BCAAs.
BCAAs 'work' because of the leucine in them. The isoleucine and valine in the mix are sort of like the mortar for the leucine 'bricks'. Leucine works because it is a key component in one of the body's signalling systems. A leucine blood level spike tells the body that you ingested a decent-sized, good quality source of protein. That signal puts the body into a more anabolic mode, which in turn means your body will either build more muscle (be anabolic) or tear down less lean mass (less catabolic).
BCAAs pre- or during a workout will stop the body from burning muscle for energy. BCAAs after a workout will, combined with the stimulus from the exercise, send a very strong signal to the body that it should build more muscle.
One key aspect of understanding how to best use BCAAs is knowing that the body only really responds to a spiked increase in blood BCAA concentration. 5 grams of BCAAs will give you a good spike, and will increase muscle growth for 90 to 120 minutes. Then you wait a few hours for blood BCAA levels to fall and take another 5 grams for another anabolic spike. Now, you might think that keeping blood BCAA levels constantly high would mean a constantly elevated rate of muscle growth. WRONG. And that's the counter-intuitive part about BCAAs. If you keep ingesting BCAAs for say, 16 hours, you will still only get that 90 to 120 minutes of growth signal. You have to 'pulse' BCAAs. The body only responds to an INCREASING level, not an INCREASED level, of BCAAs.
Ok, so knowing the above, what's the best way(s) to take them?
5 grams of BCAAs is the most you really need for a dose.
If your meals are at least 3 and a half hours apart (to allow time for amino levels in the blood to fall back to normal), taking 5 grams of BCAAs with each meal will send a stronger "there's protein available" signal, thus increasing muscle growth more than the meal alone would.
Adding 10 grams to your water you drink while working out will 'fool' your body into thinking it doesn't need to tear down muscle for energy, thus sparing lean mass (i.e. it has an anti-catabolic effect).
Sipping water with BCAAs throughout the day is not effective. It doesn't let the levels of BCAAs in the blood fall to normal, and you don't get enough at once to cause a big enough spike for the body to respond.
Now remember that 5 gram dose is NET. Most products have lots of crap in them besides BCAAs, so be sure to read the label and adjust accordingly.