Add the simple syrup, lemon juice, and water to a drink shaker and shake until well combined. Pour over ice in a large cup. Add a fresh lemon slice for a garnish if desired. Best. Lemonade. Ever. And if you like it a little more tart, cut the simple syrup down to 1/3 cup.
If you don't have a drink shaker just pour everything in the cup and stir. I use the shaker because it strains the lemon seeds out which is nice because I serve my lemonade with a straw. Straws and seeds don't mix well.
Notes
Simple syrup is even parts sugar and water heated in a saucepan over medium heat until the sugar dissolves. 2 cups sugar and 2 cups water make just the right amount to store in a quart mason jar in the fridge and will make at least a dozen glasses of lemonade.