To make any of the cocktails containing citrus juice (and that is the vast majority of them) it's necessary to balance the sour with something sweet. There are a wide variety of very sweet liqueurs that can do this - Grand Marnier or Cointreau come to mind, as in the Sidecar. But in other instances you need to put more sugar into the mix.
Some recipes will call only for sugar. Others might require superfine sugar. But the best, and certainly easiest to incorporate with other liquids is a very simple mixture of sugar dissolved in water. Various recipes abound - for a while I was dissolving two cups of sugar in one cup of water, letting it cook down until all the sugar crystals had dissolved, cooling it, then putting it in an attractive bottle. That makes fine simple syrup, but is a bit time consuming when you're ready for a drink now, but don't have proper sweetener.
I like Dale DeGroff's method for speed and efficiency. In a bottle you can seal, combine equal parts sugar and water. Shake for a minute to combine. Let sit, then shake again to be sure the sugar has dissolved. After that, your simple syrup is ready to use in cocktails. If you keep it sealed in the refrigerator, you should have no problem using it for several weeks. Mine is stored in a simple container like the one on the right - the top spout can be screwed off and it becomes a jar. The lid snaps on the bottom when you use the pour spout. When not in use, wash the spout and put it away in a drawer. Cover the jar with the lid and it takes up less refrigerator real estate. It may not be the Martha Stewart version of beautiful, but it certainly is functional and makes your home kitchen seem a little bit more like a cocktail bar. But if you get to the point of installing a speed rack for your bottles, you may have gone a bit too far.
As regular readers know, I'm a big fan of Paul Harrington and a recent fan of Dale DeGroff. They both have excellent cocktail books - Cocktail: The Drinks Bible for the 21st Century by Harrington and The Craft of the Cocktail: Everything You Need To Know to Be a Master Bartender, with 500 Recipes by DeGroff. These are great how-to books full of knowledge and experience. My other favorite personality is Alton Brown, famous for his long-running cooking show Good Eats on the Food Network.
Alton did an episode entirely on pomegranates called Fruit 10 From Outerspace. In the episode he makes grenadine out of pomegranate juice, sugar, and lemon. It's a very simple recipe but does take some time to reduce the juice to a syrup.
Here's how you do it. Combine 4 cups of pomegranate juice (try R.W. Knudsens's if you can find it), 1/2 cup of sugar, and 1 tablespoon of fresh lemon juice. Dissolve the sugar over medium heat then turn down the temperature and reduce the syrup until it's about 1 1/2 cups. It will take 50 minutes or so. Let it cool, put it in a bottle, and keep it in the refrigerator. It's like the simple syrup in that it needs to stay refrigerated or it will go bad. I made a similar syrup from black cherry juice - also delicious in cocktails or just with soda.
Many other recipes exist for making your own grenadine. Some are easier and just involve shaking a lot of sugar up with the pomegranate juice. Others start with whole pomegranates - far more work than using bottled juices. Several suggest adding a bit of vodka as a preservative, making refrigeration unnecessary. Try any of them - they don't include high fructose corn syrup or chemical preservatives, they taste great, and are a huge improvement on any type of pre-made grenadine you could buy in a shop.