1 Likes to old posts
If a person is stalking you then they might like one of your old posts by mistake. This means that the person has browsed to your old posts to stalk you and get more information about you.
2 Showing in friend suggestions
According to one theory one of the parameters that let a person show up in your friend suggestions is that they were stalking you. This also means that if you stalked someone you might appear in their friend suggestions.
3 They see your stories
One of Facebook features is called stories. When you post a story about yourself you can actually see how many people viewed it and who exactly saw it. Post stories to know who stalks you.
4 They are following you
If you have enabled followers on Facebook then you can easily find out who is following you. Some of your followers might actually be stalkers.
5 Random likes
If a person is already on your friend list and hardly likes your posts then one random like might indicate that this friend was actually stalking you for a long period of time.
6 More common friends
Stalkers can in many cases try to increase the number of common friends between you and them. If the common friends between you and another person are constantly increasing then this person might be stalking you.
7 They show up among the nine friends
According to one theory one of the parameters that determines the 9 friends that show up in your profile is whether this person was stalking you or not. According to this theory if a person stalked you then they might show up in the friends box. (See How does Facebook friends suggestion work?)
8 Accidental likes
If a person is stalking you then they might make an accidental like by mistake. Getting one of those likes by a stranger is a clear sign that you were being stalked.
9 They know your news
If you realized that someone knows your news even though you haven't been talking then probably that person was stalking you on Facebook.
10 They know a lot about you
If during a conversation you realized that someone knows a lot about you then there is a possibility that this person was stalking you. (See Why do people post everything about their lives on Facebook?)