You override the Validate method from ElementValidatorBase, where you have IElementValidatable interface as parameter.

public override bool? Validate(IElementValidatable targetElement)
{
    var submittedValue = targetElement.GetSubmittedValue() as string;

    //validate submittedValue.
}

after that you kan override BuildValidationModel method to build the model and pass the validation message you want.

public override IValidationModel BuildValidationModel(IElementValidatable targetElement)
{
    if (_model == null)
    {
        _model = base.BuildValidationModel(targetElement);
        _model.Message = _localizationService.GetString("/episerver/forms/validators/elementselfvalidator/unexpectedvalueisnotaccepted");
    }
    return _model;
}

You can also access the model when inherting ElementValidatorBase with "_model" property.

I hope this helps :-) 

In the Validate() method in your validator, you should be able to cast targetElement as your custom element type which should allow you to access the properties set on the element. For example:

public class TestValidator : ElementValidatorBase
{
    public override bool? Validate(IElementValidatable targetElement)
    {
        if (targetElement is MyCustomElementType myElement)
        {
            //add your validation here
            var submittedValue = targetElement.GetSubmittedValue() as string;
            return (submittedValue.Contains(myElement.submittedValueShouldntContainThisPropertyValue));
        }
        return true;
    }
}