TestController.cls

public with sharing class TestController {

    public String output { get; set; }

    public PageReference run() {
String url = 'https://na1.salesforce.com/services/data/v23.0/chatter/feeds/news/me';
            
HttpRequest req = new HttpRequest();
            
req.setMethod('GET');
req.setEndpoint(url);
req.setHeader('Content-type', 'application/json');
req.setHeader('Authorization', 'OAuth ' + UserInfo.getSessionId());
            
Http http = new Http();
  
HTTPResponse res = http.send(req);
 
output = (res.getBody());
        return null;
    }

}

x.apexp

<apex:page controller="TestController">
<apex:form>
<apex:commandButton action="{!run}" value="Save" id="theButton"/>
{!output}
</apex:form >
</apex:page>