To display error messages in the Visualforce page add below tag where you want to display the error message.

Visualforce page:

<apex:pageMessages />

Apex Controller:

ApexPages.Message myMsg = new ApexPages.Message(ApexPages.Severity.ERROR,'Error Message.');
ApexPages.addMessage(myMsg); 

(Or)

ApexPages.addMessage(new ApexPages.Message(ApexPages.Severity.ERROR,'Error Message.'));

Sample Code:

Visualforce Page:

<apex:page controller="SampleVisualforcePageController">
    <apex:pageMessages id="errMsg"/>
    <apex:form>
    	<apex:commandButton value="Show Error Message" action="{!showErrorMsg}" reRender="errMsg"/>
    </apex:form>
</apex:page>

Apex Class:

public class SampleVisualforcePageController {
    
    public void showErrorMsg() {
        
        ApexPages.addMessage( 
            new ApexPages.Message( ApexPages.Severity.ERROR, 'Some Error Occurred' ) 
        );
        
        ApexPages.addMessage( 
            new ApexPages.Message( ApexPages.Severity.INFO, 'Some Info' ) 
        );
        
        ApexPages.addMessage( 
            new ApexPages.Message( ApexPages.Severity.WARNING, 'Some Warning' ) 
        );
        
        ApexPages.addMessage( 
            new ApexPages.Message( ApexPages.Severity.CONFIRM, 'Confirm Message' ) 
        );
        
        ApexPages.addMessage( 
            new ApexPages.Message( ApexPages.Severity.FATAL, 'Fatal Message' ) 
        );
        
    }
    
}

Output: