Most people aren't aware of their core beliefs and how they affect their thoughts, feelings, perceptions, etc. on a daily basis. I'm going to borrow a definition of core beliefs from someone else because a full exploration of the concept is beyond the scope of this post. According to Lynne Forrest (found at http://lynneforrest.com/html/core_beliefs.html), core beliefs are "deeply rooted convictions...[that]...originate in childhood and become the lens through which we view ourselves and the world around us. These basic, but often erroneous notions rule and limit us until we bring them into consciousness and begin to challenge them."
So the first step is being aware of your beliefs. Here are some indicators that you ascribe to the belief that you need a partner in order to be happy:
1. When you're not seeing anyone you feel compelled to "get out there" and date and/or you're constantly on the lookout for a potential partner.
2. When you are seeing someone you become very anxious, especially if he/she doesn't call or contact you regularly. You worry that he/she will lose interest in you. You worry about "losing" him/her -- this is a sure sign that implicitly you believe you need him/her (or some other partner) in order to be happy.
3. You don't feel content unless you are dating someone. (You feel discontent or unhappy when you're not seeing anyone).
4. You stay in an unhappy relationship because you're afraid to be alone.
5. You're a serial monogamist -- as soon as one long-term relationship ends you move immediately into another one with little time in between. Or you don't end one relationship until you have a prospect for another relationship lined up.
6. When you feel sad or lonely you think to yourself, "I wouldn't be feeling this way if I had a boyfriend/girlfriend/husband/wife/partner."
7. You feel bad when someone asks you if you're seeing anyone and you have to say no.
8. When you're not seeing anyone you feel like "something's missing." When you are seeing someone you feel fulfilled or complete.
9. You worry that something is wrong with you because you haven't found the person you're supposed to spend your life with.
This list certainly isn't exhaustive and I will try to add to it as ideas come to me. Also, feel free to give me suggestions by leaving a comment.