Sample Code1:

Visualforce page:

<apex:page docType="html-5.0" controller="Sample">
<apex:form >
    <apex:pageBlock >
        <apex:pageBlockSection>
            <apex:pageBlockSectionItem>
                Date: <apex:input type="date" value="{!dat}"/>
            </apex:pageBlockSectionItem>
        </apex:pageBlockSection>
    </apex:pageBlock>
</apex:form>
</apex:page>

Apex Controller:

public class Sample {
    public Date dat {get;set;}
    public Sample() {

    }
}

Output:

Sample Code2:

Visualforce page:

<apex:page controller="datePicker" id="mypage">
    <apex:form>   
        Date: <apex:inputText value="{!datename}" size="10" id="demo" onfocus="DatePicker.pickDate(false, this , false);" />   
    </apex:form>
</apex:page>

Apex Controller:

public class DatePicker
{
    public String datename {get; set;}
}

Output: