For many people, the very idea of needing to search for alien artifacts is ludicrous. After all, alien spacecraft can be seen in the skies of Earth every day of the week, and virtually every archaeological specimen older that three thousand years was fabricated, if not by extraterrestrials, then by dim-witted humans under the guidance of extraterrestrials. So for people who think along those lines, there's nothing to search for: the Earth is already overflowing with alien artifacts. But scientists (who are part of the Conspiracy) aren't allowed to admit that -- they have to look further afield. I've just been reading three fascinating articles on the subject at arXiv.org:
The first paper is called On the likelihood of non-terrestrial artifacts in the Solar System. It's based on the idea that the most probable type of artifact would be an unmanned space probe between 1 and 10 metres in size. The authors use my favourite mathematical formula, Bayes' Theorem, to estimate the probability that such a probe exists in the Solar System but has not yet been detected (I'm annoyed by this, because I could easily have done the calculation myself, but I wasn't clever enough to think of doing it). They conclude that the probability that there are no NTAs ("non-terrestrial artifacts") waiting to be found on the surface of the Earth is 75%, that there are none on the surface of the Moon is 65%, and that there are none on the surface of Mars is 50%. But when it comes to the remainder of the Solar System, it's a different matter altogether: the authors say they "have almost no confidence that NTAs are absent".
There is a natural tendency to assume that any advanced alien civilization would send out interstellar space probes, just as we would ourselves if we had the money. But what if the aliens simply stay at home and mind their own business? We might still be able to detect their "artifacts", as shown in the second paper: Detection Technique for Artificially-Illuminated Objects in the Outer Solar System and Beyond. In this case, the artifacts in question are city lights. The night-side of the Earth (the side facing away from the Sun) is covered in bright little pinpoints of light -- and these add up to quite a lot of light coming from a place that, according to the laws of nature, should be pitch black. Any planet with a reasonably advanced civilization is likely to be the same, giving it a characteristic signature in terms of both the intensity and the spectrum of the light emitted.
The first two papers assume the aliens are at the same technological level as ourselves, or slightly ahead of it. But what if they were millions of years ahead? A really advanced civilization might be capable of harvesting the entire energy of a star, or of manipulating the structure of space-time. This possibility is addressed in the third paper: Black Holes: Attractors for Intelligence?