I start with this fact. Meringues can be difficult. But, if you know the rules going in, they are can be a simple pleasure.
2 parts sugar (granulated or 1/2 granulated & 1/2 confectioners)
1 part egg white (only egg whites and if this means pressing the whites through a CLEAN fine sieve, do it)
A bit of lemon juice (You can rub this in a bowl. I work in CLEAN glass, it provides the most promise.)
Start with the whites on low with a hand mixer. When the whites are fairly frothy, mix in 1/4 of the sugar, mix to a stiffer state and add the rest of the sugar a little at a time. You'll want to mix these until they're very stiff. When you think they're ready, test a small amount between your fingers for smoothness. If they aren't smooth, keep beating. When you have smooth, stiff peaks, pipe out the size you wish onto a lined baking sheet. Bake at 225 degrees F for about 30 minutes. If, at that time they are stiff but a bit sticky, turn the oven down to 175 degrees for another 30 minutes and let them finish drying. Humidity in your home will determine drying time. Meringues may be kept, air tight for a couple of weeks.
I love to plate them over a raspberry or strawberry coulis. Made small, they can be cookies. There are many other inspiring methods for serving. Pavlova style. With shaved chocolate and on a plate decorated with syrup. Under or over ice cream. With a flourish of fresh seasonal fruits.
The most important things to remember about meringues are: CLEAN bowl and utensils, you need a little ACID (cream of tartar or lemon juice unless you work in a copper bowl), NOT a speck of egg yolk or any other fat, cook to done and then dry at a low temp.
Here I'll share that practice is the best teacher. I also love consulting the experts like: COOKS ILLUSTRATED - America's Test Kitchen, Julia Child (cream of tartar) or Alton Brown or any of the myriad internet options at your hand.