When have the police officially begun a "search?" This is an important question because the Fourth Amendment explicitly says that the people are protected from unreasonable search and seizures. Now, the police need to search and seize property given their jobs -- but the people have a right to privacy and protections against a search and seizure that is deemed illegal in the eyes of the law.
So let's answer the question posed above. When have the police officially and legally "searched" property? There are two factors that need to be discussed here. The first is "did the person who was targeted by the search have an expectation to privacy?" The second is "was the person's expectation of privacy reasonable?" If the answer to both questions is "yes," then the police violated your Fourth Amendment rights. If the answer to either question is "no," then they have performed a search.
There are other circumstances though that grant police the ability to search property. A search warrant is the most notable, which gives them the legal authority to search your property without notice or consent. Another notable example is if you consent to letting the police search your premises. Yet another example is if the police search property for the sake of their safety or the safety of others.
Despite the number of legitimate and legal ways that the police can search and seize property, there are still plenty of examples of them doing it illegally anyway. When you have been subjected to an illegal search and seizure, you need to consult with an attorney immediately.