[SalesForce] How to make a picklist input field as required in a Visualforce page

We can do this using two different approach :

1. Using Actionfunction of VF and then rerender the outputPanel containing our text field https://developer.salesforce.com/forums/?id=906F000000096tTIAQ
2. using Javascript to input the text in text input https://stackoverflow.com/questions/1085801/get-selected-value-in-dropdown-list-using-javascript

Any Rerender attribute you use in vf page, should point to an id of an apex component like <apex:outputPanel />,<apex:form />,<apex:pageBlock />,...so on.

<apex:actionFunction ... rerender="inputScreenPanel"></apex:actionFunction>

<apex:outputPanel id="inputScreenPanel">
    //apex components to be rerendered
    <div id="input-screen" class="input-box">
       ...
    </div>
</apex:outputPanel> 

NOTE : <button /> tag inside <apex:form /> behaves like form submitter button(<button type="submit"/>), so you should explicitly set the type="button" as shown in the example.

Here is an simple example to rerender dynamic input field:

VF:

<apex:page controller="AccountController">
    <apex:form>
        <button type="button" onclick="update()">update</button>

        <apex:outputPanel id="inputScreenPanel">
            <apex:inputField id="input-field" value="{!currAcc[apiName]}"/>
        </apex:outputPanel>

        <apex:actionFunction name="update" action="{!updateAcc}" reRender="inputScreenPanel">
        </apex:actionFunction>
    </apex:form>
</apex:page>

Controller :

public with sharing class AccountController {
    public List<Account> acclist{get;set;}
    public Account currAcc {get;set;}
    public String apiName {get;set;}

    public AccountController(){
        acclist = [SELECT Id,Phone,Name FROM Account WHERE Id IN ('00128000002kbKS','00128000002kbKT')];
        currAcc = accList[0];
        apiName = 'Name';
    }

    public PageReference updateAcc(){
        currAcc = acclist[1];
        return null;
    }
}