I call this the never ending blanket because another blanket is started before the last one is finished. I keep several bags of smaller balls of yarn in certain color combos. These may change as I get more of certain colors and less of others. The color combos I usually use are bright colors, pastels, and red, white and blue. I only use worsted weight yarn but even then some are too thick or thin so make sure they're all about the same although some variation can be worked with.
You can use any plain granny square pattern. I use one that doesn't have a lot of holes. I also use a K hook so these squares go fairly quickly. Since I am making them for Project Linus and kids come in all sizes I don't worry too much in the beginning about size and number of squares. I found if I have a lot of smaller balls making more small squares works. On the other hand, if you have larger balls you can make large squares and don't have to make so many.
The pattern for my square can be found here.
I have a few "rules" I follow, but you don't have to
1. Never change colors in the middle of a row. If I don't have enough I unravel and try on a lower row of another square.
2. Never do more than 2 rows with the same color in the same square.
3. Except in the very beginning where sometimes it's unavoidable, once I choose a ball to use , I use it up. In other words it may be big enough to make a row 7 and 8 of one square, 6 and 7 of another then maybe a 2 or 3 and finally to use it up I make one or two row 1's. This is the rule that makes it a never ending blanket, there are always squares started for the next blanket.
4. When first starting your blanket, start with the smallest balls first. This makes it easier to use up all those small balls and work your way up. If you want, save any pieces that are too small to make a first row for fringe.
5. As you get more scraps, small balls etc. add them to the squares you have made, at some point as your working on them, you have to decide how big you are going to make the squares and how many you are going to need.
6. Once you have enough join them together in a pleasing way. I often do all the last rows in the same color. In the picture above, if you can make it out, I did the last rows of all the squares on the bright ones in Red Heart Mexicali variegated. This can pull all those colors together. But again, you don't have to.
7. Do several rows of double or single crochet for the border.
Now that your finished, if you followed the rules, you should have at least a couple squares of the next blanket started. You don't have to do them all at once, or save up a lot of yarn. I usually add scraps as I get them so it can sometimes take a while to complete a blanket but of course I'm working on a lot of other projects so I'll have more scraps!!