1. If he or she sudenly begins to text and call you relentlessly, this is a strong sign that they probably haven't moved on and want to get back with you. If they've moved on emotionally, they would not be communicating with you.
2. If your ex girlfriend or boyfriend still want to get together with you at your local hang out or social events, this could mean they want to get back with you but, do not read more into the situation than what is there, they might just want to stay friends with you.
3. If mutual friends keep telling you that your he or she is always asking about you, it could be a possibility they would like to get back together with you. But bear in mind, they might just want to stay friends with you, it really depends on how they are acting. Just use a little common sense, and do not jump to conclusions. If they are continually asking if you are with another person, and or, getting possessive and jealous, this is a good example of what I mean.
4. If, when you do get together, or hang out, they reminisce about how the relationship could have been, they might just be looking into the possibility of getting back with you if they know you still have feelings for them.
NOTE: You need to consider some things before getting back together with your ex-girlfriend or boyfriend, are you getting back together for the right reasons? If you're just lonely or desperate, or, heaven forbid, you're trying to spite them, then be advised, do not get back together with your ex because you'll regret it later.
If you refuse to consider the reason why you two are getting bact together, you will sooner or later break up again because you are returning to each other without dealing with what broke you up.