If you want to be technical, humans have already attempted to make contact with alien civilizations. Once on purpose, and also at a non stop rate with our various forms of communications that go into space. Should we make a direct attempt to make contact with an alien civilization? The answer to that is no. We can look at the reasons why the answer is no.
First let's look at the previous attempt that was made. During 1977 the Voyager 1 was launched with a golden record aboard. It had various sounds and pictures of Earth. It left our solar system in November 2004. It is meant to be "found" by an alien life form.
Second we have all the radio, television, and other forms of communication signals that we have been beaming into space in all directions for the last 100 plus years. If a civilization were to base their opinion of the human race on these signals, it would not be good for us. Think about the movies that come out of Hollywood every year. Of course we know that these are works of fiction, but would an alien civilization? If we look beyond what we consider entertainment, what about the good old fashion evening news? Very rarely does the news ever show anything good. If it is, it is no more than a sound byte before the commercial break. Most of the news shown is about war, famine, atrocities and other items that television stations decide have shock value.
Overall, the wayward signals do not paint a very convincing picture. In no way would an alien civilization think that the inhabitants of this blue planet are peace loving and mean no harm.
Another factor that we can look at is the alien civilization itself. There are 3 options for the aliens. The middle choice is not very likely (statistically speaking).
1. The alien civilization is much more advanced than we are. This is a likely scenario if for no other reason than they found us. This would mean they have the technology to receive/transmit signals over vast distances faster than we do. If it is an actual physical encounter then they have reached a point where space travel is used. In that area, humans haven't even tested the water with their toes. The farthest we have gone (on a manned mission) in space is our moon. That is a pitifully small distance on the scale of interstellar space travel.
If the aliens are more advanced, we could very easily be seen as wild dogs that need to be put down. We fight among ourselves non stop and have since the origins of human history. Another thing to think about was brought up by one of the great minds of our time. Stephen Hawking said (paraphrasing) that when the Native Americans came into contact with a more technologically advanced society (the Europeans), it did not turn out very well for the Native Americans. It is not a stretch to believe that a similar situation could occur with two alien races meeting for the first time.
2. Both Humans and the alien civilization are on the same level of technology. This is not very likely. If both races are at the same level, neither would be capable of interstellar travel or communication in real time. The extreme time lag for a message to reach the target and an answer to return could stretch into a generational time span.
3. We have the upper hand in the technology field. If it were in the near future, at a time that we were able to travel the stars, dropping in on an alien civilization could create an entire host of problems for the aliens. We would be god-like to them. If humans were perfect, we could use our knowledge to help them and bring them up to speed. Of course even this is a moral dilemma. What if they are not mature enough (as a race) when we start to dump all this technology on them. It could be like giving a small child a machine gun.
More than the machine gun scenario, humans have shown, throughout their history that they are not good Samaritans. Of course there are good people, but taken as a whole, the human race is almost evil. If we ran into a race of aliens that were at the level of Ewoks from Star Wars (just a random example) there is a very good chance humans would do what they have always done. Enslave the population and take any resources that we want or need.
So taken as a whole, it is probably not a good idea to initiate contact with an alien civilization. If they try to contact us, should we shy away and ignore them? Of course not. One, it may start a war in space, two (and more importantly) how could it ever be a possibility to turn away from the answer to a question that man has asked for centuries: Are we alone? Having absolute proof that there is other intelligent life is too good of an opportunity to pass up. At our current mindset, it is probably better to let the aliens make the first contact. We are not ready to go poking around a neighborhood we know nothing about, especially when we haven't even seen the fence to our own back yard yet.