How can you tell if a series is absolutely convergent or conditionally convergent?

How can you tell if a series is absolutely convergent or conditionally convergent? I am only able to tell if it's convergent and that's it. I read my book and noticed that if you rearrange terms with negative signs, then the sum could change but I don't see how that works in practice so it would be great if someone can compare and contrast the two cases for me.

Any input would be greatly appreciated!

Thanks in advance!