Insecurity is the fear of losing the stability of the relationship in this particular case. She's worried that it won't work out, or that you'll reject her for someone else. This fear is NEVER a good thing. All the girls I know want security, amongst other things.
A stupid guy can desire to make a girl insecure very easily. He will spend time talking to his girlfriend about all his past girlfriends, his girl friends, spending time talking wistfully about what it was like when he was single, or telling lies about where he was or what he was doing. He can also act in an untrustworthy manner (not answering questions, telling lies, theft etc. ) Like I said, he would have to be stupid to act like this. DON'T BE STUPID!
Insecurity is a feeling of doubt or fear caused by perceived unreliability. Therefore, you can make someone feel insecure by being unreliable and making her feel uncertain about your motives, whereabouts or feelings. I think it is a very bad thing and is pretty much sure to ruin your relationship or friendship, so I do not recommend attempting to make anyone feel insecure. Why would you want to cause someone such distress? As CUDAGTO said, it is likely to come back to you, especially if you get a reputation for being unreliable and unreadable.
Insecure is when a person doesn't feel like they are in control of anything? There are many ways to make someone feel insecure, if you are in a relationship, having other girls around usually works. If you do this , I don't know why you would, be careful that you don't mistake making her feel insecure with being cruel or mean. What you sent out will come back to you times three! Are you ready for that?