>>My knitting bag has leftover yarn that I want to make squares with. My grandma gave me a book titked "440 More Knitting Stitches". It shows you how to do things like knit stripes and diamonds, cable knitting, stars, and even lace. <<

Wow!

>> I'm thinking of picking different patterns to try, making one square of each, and eventually making it into a blanket.<<

What a great idea! You can also make a vest or sweater that way.

>> I'm going to have to see if I can find patterns that will work together, or at least not clash though. And I might need to make sure my yarn is the right thickness for the patterns. I feel like thick yarn would be to clunky for some of them.<<

Check the pattern. They often tell you what weight of yarn to use, especially in knitting. You can also consult a general yarn guide.