The method I use gets very clean sand (no cloudiness at all!) but is messy and wastes a lot of sand. Since I use super cheap play sand, this doesn't bother me much. But if you're using the fancy stuff from the pet store, don't try this at home! Well, not unless you're rich.
I do this outside. I use a 3 gallon bucket. I put about 2 or 3 inches of sand in the bottom. I have a nozzle on my garden hose that allows for a single pressurized stream of water. I aim the the water at the sand and blast it to kingdom come! I make sure to blast each area of the bottom, and make sure that the spray moves all the sand so that I can actually see the bottom of the bucket where the water spray is aimed (if that makes sense). It helps to have a bucket that is a much different color than the sand. (I use tan sand and a blue bucket.) That way I know I'm getting all the sand up and moving around. When there's about 3 inches of water above the sand, I stop the water and immediately tip the bucket and pour off the dirty water. I repeat this about 5 or 6 times. You'll start to see when the water isn't as cloudy. Then for about 5 or 6 times, I squat down and actually get the nozzle down in the sand, making sure to really move the sand around with the force of the water and being sure to get all areas. Again, I pour off the water immediately after switching off the spray. Then when I can see the water is getting kinda clear, for maybe 5 or 10 times I let the water and sand settle for about 10 seconds before I pour off the water.
I strongly recommend eye protection! This method sometimes shoots sandy water into the air, if you hit the side of the bucket right. I use sunglasses. And, bonus, you'll look cool.
Then I scoop the sand into an empty tank. I put a bowl on the sand, and pour water into the bowl to fill the aquarium.
With this method, I get crystal clear water from the start. I have used this method on different tanks ranging from 10g to 55g, and always have excellent results.
For a 75g tank, I would recommend 3 bags of play sand, which will cost you about $9 to $12. The only real downside to play sand is that it only comes in shades of tan (which varies between brands but also varies between batches of the same brand), at least where I am. This method also works with pool filter sand and blasting sand, which are more expensive. I have no experience with these types, and I would be very careful about the sharpness/abrasiveness of these products.