Our home is one of the most intimate and well protected rights we have under the fourth amendment and the constitution. Allowing us to be free from unreasonable search and seizure in our house, apartment, and even motorhome, means that law enforcement must have a warrant in order to search our home or arrest us in it. There are several exceptions, however.
While it is true that officers must obtain an arrest warrant from a judge or magistrate before arresting us at home, being in the yard, or even on the front doorstep does not offer the same protections. A common ploy is for officers, without a warrant, to wait for an individual to come home or leave the house and walk to a car.
In order to search within the home, an officer must go to a judge or magistrate, setting forth in a sworn affidavit the details as to what will be searched and why, outlining the probable cause and suspected criminal activity. If the judge or magistrate agrees with the determination of probable cause, then the search warrant is signed.
The law allows officers to ask the judge or magistrate for a 'no knock' warrant, under certian circumstances. Normally, officers armed with a search warrant must announce their presence and show the paperwork to the suspect (owner of the home to be searched). However, with a no knock search warrant, officers can essentially force their way into a home with no warning at all. The law should be extremely limited in that regard, as a no knock warrant is extremely intrusive and dangerous.
Without a search warrant, officers can still search your home in two main ways. First, a consent search allows officers to enter your home and search without a warrant. Second, under exigent circumstances (emergency), officers may enter a home without a warrant. For instance, if a suspect is fleeing a crime scene and runs into their home, officers may pursue the suspect into the house without a warrant, assuming they are in hot pursuit. Likewise, in an emergency, such as a 911 call for help, officers may enter a home to provide services.