A spoon may seem ideal for stirring peanut butter, but natural peanut butter is so gloopy that it could easily get caught in the bowl of the spoon. A sturdy butter knife is ideal for getting into the crevices of a peanut butter jar, and when done, you can simply scrape off the excess on the rim of the jar.
Slowly insert your butter knife into your jar and stir. If the jar is quite full, you'll have to go slow to avoid spilling. Keep stirring until some of the oil is combined, then you can start going a little more vigorously. Keep stirring and smearing some of the big chunks against the inside of the jar, and you'll have perfectly homogenous peanut butter in no time.