Measure your counter height. Allow for about 10 inches of legroom space between the stool and the counter.
Make a budget for how much you'd like to spend on the stool. Most likely you will be getting at least two stools, so account for that when crunching your numbers.
Make a list of a few stores that carry items within your budget and have a wide variety of styles.
Take into account the comfort of the stool you want. Anything with a cushion, back and armrests will be comfortable enough to sit on for long periods. Many simple and modern stools come equipped with cushions these days.
Consider color, finish and style. You can either match the stool to the wood color of your cabinets or go for contrasting shades and wood finishes. Think about whether you are going for a contemporary look or a more traditional style.
Think about fit. When you pick the stool you want, make sure the size will be compatible with the space you have in your kitchen. Measure the area where the stools will go to allow for moving room when the stools are in place.