Calling the REST API in javascript using forcetk is pretty straightforward in a content script:

function processSessionID(sessionID) {

    var client = new forcetk.Client();
    client.setSessionToken(sessionID);

    client.query("SELECT Id, Name FROM Opportunity", function(response){
        // do something with response, response is a list of Opportunities in this case
    });         
}

Using it from a popup seems a little more involved. Firstly, I think you would need to use a content script to setup the forcetk client and interact with Salesforce. Then, from your popup, you'd have to use messaging to communicate back and forth. For example, in your popup.js:

chrome.tabs.query({active: true, currentWindow: true}, function(tabs) {
  chrome.tabs.sendMessage(tabs[0].id, {method: "getOpportunities"}, function(response) {
    console.log(response.opps);
  });
});

Then, in your content script, add a listener:

var client = new forcetk.Client();
client.setSessionToken(sessionID);

chrome.runtime.onMessage.addListener(function(request, sender, sendResponse) {
    if(request.method === 'getOpportunities') {
      client.query('SELECT Id, Name FROM Opportunity',function(response) {
        sendResponse({opps: response});
      }
    }
  });

Calling the REST API in javascript using forcetk is pretty straightforward in a content script:

function processSessionID(sessionID) {

    var client = new forcetk.Client();
    client.setSessionToken(sessionID);

    client.query("SELECT Id, Name FROM Opportunity", function(response){
        // do something with response, response is a list of Opportunities in this case
    });         
}

Using it from a popup seems a little more involved. Firstly, I think you would need to use a content script to setup the forcetk client and interact with Salesforce. Then, from your popup, you'd have to use messaging to communicate back and forth. For example, in your popup.js:

chrome.tabs.query({active: true, currentWindow: true}, function(tabs) {
  chrome.tabs.sendMessage(tabs[0].id, {method: "getOpportunities"}, function(response) {
    console.log(response.opps);
  });
});

Then, in your content script, add a listener:

var client = new forcetk.Client();
client.setSessionToken(sessionID);

chrome.runtime.onMessage.addListener(function(request, sender, sendResponse) {
    if(request.method === 'getOpportunities') {
      client.query('SELECT Id, Name FROM Opportunity',function(response) {
        sendResponse({opps: response});
      }
    }
  });

PS. I haven't tried this but seems like it should work.

Calling the REST API in javascript using forcetk is pretty straightforward:

function processSessionID(sessionID) {

    var client = new forcetk.Client();
    client.setSessionToken(sessionID);

    client.query("SELECT Id, Name FROM Opportunity", function(response){
        // do something with response, response is a list of Opportunities in this case
    });         
}

Calling the REST API in javascript using forcetk is pretty straightforward in a content script:

function processSessionID(sessionID) {

    var client = new forcetk.Client();
    client.setSessionToken(sessionID);

    client.query("SELECT Id, Name FROM Opportunity", function(response){
        // do something with response, response is a list of Opportunities in this case
    });         
}

Using it from a popup seems a little more involved. Firstly, I think you would need to use a content script to setup the forcetk client and interact with Salesforce. Then, from your popup, you'd have to use messaging to communicate back and forth. For example, in your popup.js:

chrome.tabs.query({active: true, currentWindow: true}, function(tabs) {
  chrome.tabs.sendMessage(tabs[0].id, {method: "getOpportunities"}, function(response) {
    console.log(response.opps);
  });
});

Then, in your content script, add a listener:

var client = new forcetk.Client();
client.setSessionToken(sessionID);

chrome.runtime.onMessage.addListener(function(request, sender, sendResponse) {
    if(request.method === 'getOpportunities') {
      client.query('SELECT Id, Name FROM Opportunity',function(response) {
        sendResponse({opps: response}); 
      }
    }
  });