You will first need to use a controller or extension with your vf page depending on your requirement(Assuming you are already using). Then you will need to associate an action fucnction with the search button.
In your controller you will need to have variables which you have bound with the inputText.
in your apex page tag:
<apex:page controller = "MyController">
or
<apex:page standardController="Applicant__c" extensions= "MyController">
On the Button:
<apex:commandButton value="Search" action = "{!searchRecords}"/>
In the inputText Tag
<apex:inputText value="{!strSkillSet}"/>
<apex:inputText value="{!strKeyWords}"/>...
in your controller:
public Class MyController{
string strSkillSet {get;set;}
string strKeywords {get;Set;} // declare variables for others similarly
}
and the below method
public List<Applicant__c> searchRecords(){
return [Select Id, Name from Applicant where yourfieldName =: strSkillSet and/or yourfieldName =:strKeyWords ...];
}