<apex:page controller="TestCommandButtonController">
    <apex:pageMessages />
    <apex:form >
        <label>Text</label>
        <apex:outputPanel>
            <apex:inputText value="{!text}"/>
            <apex:actionSupport event="onchange" action="{!refreshText2}" reRender="text2Input"/>
        </apex:outputPanel>
        <label>Text2</label>
        <apex:inputText id="text2Input" value="{!text2}" rendered="{!text=='Other'}"/>
        <label>Text3</label>
        <apex:inputText value="{!text3}"/>
        <apex:commandButton action="{!sampleButtonHandler}" value="Sample Button"/>
    </apex:form>
</apex:page>