If the police show up at your house with a warrant to search it, they will likely knock on the door, inform you of the warrant and tell you to open up. You are legally obligated to do so since they got the warrant from a judge, and police can, in many cases, force entry if you refuse.
But what if they do not have a warrant? Getting one takes time and can be difficult. The first step for many officers is simply to ask if they can come in and talk to you and/or take a look around. You can ask them if they have a warrant, and they have to be honest with you. If they tell you that they do not, do you need to open the door?
You do not. There are a few exceptions — such as when officers believe someone is in danger or that a crime is in progress and there’s no time to get a warrant — but they generally have no right to enter if you do not want them to. It’s not illegal to tell them so. You can be kind and polite, just telling them you’d rather that they don’t come in and that they can come back with a warrant if need be.
Most of the time, the officers will leave, either because they know they can’t enter or because it’s time to go get a warrant. There have been cases, though, where they still enter the house. If you got arrested after this sort of entry and you believe your rights were violated, you must know what options you have for your defense. Don’t let a warrantless search ruin your future without a fight.