<apex:page controller="HeddyLoginController">
    <apex:form>
        <apex:pageBlock title="Login to Heddy">
            <apex:pageMessages/>
            <apex:pageBlockButtons>
                <apex:commandButton value="Search" action="{!login}"/>
            </apex:pageBlockButtons>
            <apex:pageBlockSection>
                <apex:inputfield label="Heddy username" value="{!ps.HeddyUsername__c}"/>
            </apex:pageBlockSection>
            <apex:pageBlockSection>
                <apex:inputSecret label="Heddy password" value="{!ps.HeddyPassword__c}"/>
            </apex:pageBlockSection>
        </apex:pageBlock>
    </apex:form>
</apex:page>

public class HeddyLoginController {

    public String baseEndpoint = 'https://api.Heddy.com/lkapi/';
    public HeddySession__c ps { get; set; }


    public void HeddyLoginController() {
        ps = [SELECT APIAuthorizationKey__c from HeddySession__c LIMIT 1];

        if (ps == null) {
            ps = new HeddySession__c();
            try {
            insert ps;
            } catch(System.DMLException e) {
            ApexPages.addMessages(e);
            ApexPages.Message msgErr = new ApexPages.Message(ApexPages.Severity.ERROR, 'Error! We are unable to save your session in Salesforce.');
            ApexPages.addmessage(msgErr);
            }
        }
    }

public HttpResponse fetch() {
        Http httpProtocol = new Http();
        HttpRequest request = new HttpRequest();
        HttpResponse response;

        String authpoint = '/authtoken?user=' + ps.HeddyUsername__c  + '&pass=' + ps.HeddyPassword__c;

Attempt to de-reference a null object