It can be frustrating to be a libertarian. It might be a little less frustrating than it was a few years ago, because more people have been exposed to libertarianism, particularly through Ron Paul and the internet. However, there are still a lot of misconceptions out there. The essence of libertarianism is that you don't believe in the initiation of force for political or social change (just as the Libertarian Party's pledge says). You can hold this view regardless of your personality and characteristics.
Many libertarians find themselves in debates with others, particularly because they are so passionate about their views. It is hard to "convert" someone. Libertarians who are well-versed on all of the major issues have trouble convincing others. Imagine how hard that makes it for libertarians who are not as knowledgeable.
You will probably not win someone over by debating them. Debates tend to drive people the other way. They become more stubborn in their position. They do not want to be wrong, just as you don't want to be wrong. With that said, there are legitimate reasons to engage others in (hopefully friendly) debates.
If you have an audience, a debate with someone can be useful in swaying the observers. They may not be that opinionated one way or the other. If you lay out good reasons for your philosophy, it might help the people listening move closer to your point of view.
Another reason to debate someone is to sharpen your own skills. The other person may have some arguments that you have never heard before. They may challenge you on some of your beliefs. They may try to point out inconsistencies. This is good for your own knowledge. It can help sharpen your own ideas, even if you have to think about it later, after the debate.
Of course, one last reason to debate someone is just for your own satisfaction of "winning the argument" and getting some jabs in at the other person. If you are doing this though, you are highly unlikely to change the other person's mind.
The hardest thing for a libertarian to do is to convince close friends and family members, particularly the latter. Family members know you well. They know your faults. They probably do not think you are a genius and you probably aren't. They will have trouble seeing the merits and consistency of your libertarian philosophy, especially if they are already far away from it. If you want to engage in a little friendly debate with family members, make it minimal. Just try to explain your point of view without attacking theirs. You will probably not change any minds. You can lead the horse to water, but you can't force it to drink.
If you are going to discuss libertarianism with others, it is actually best to do it with others who are already sympathetic to your ideas. Your goal is to strengthen their understanding. You are not going to change a statist into a libertarian overnight. You can help someone who is quasi-libertarian become slightly more libertarian and slightly more skeptical of the state. There are usually no home runs. You have to advance one base at a time, and even this can be difficult.
If you really want to help the cause of liberty, make sure that you are virtually an expert yourself. I see so many people trying to change the world, when they need to change themselves first. They are putting the cart before the horse. If there are libertarians who have been studying the subject for 20 years and speaking in front of audiences who can't convince others, why would you think you can if you have just been reading a couple of articles a day for the last 6 months?
Be sure that you have a great grasp of the issues and that you are consistent in your philosophy. Then you can talk to others and convey the right information. There is nothing I hate to hear more than listening to someone trying to convince another person of libertarianism and conveying the message in a poor way.