Wire the ESP-01 as follows. Go ahead and leave your TTL converter connected so you can continue programming and debug.

Connect your ESP-01 to your TTL serial converter and flash your ESP-01 with NodeMCU

Follow Marc's good instruction on how to load NodeMCU onto your ESP-01 at https://importhack.wordpress.com/2014/11/22/how-to-use-ep8266-esp-01-as-a-sensor-web-client/

ESPlorer is a great way to program the ESP-01. Get ESPlorer IDE running, so you can access and program the ESP-01.

http://esp8266.ru/esplorer/

Program your ESP with the following code -

Change the ip address of the M:connect command to match the ip address of your MQTT broker.

-- Garage Door controller version 2/15/15 pete@hoffswell.com
-- GPIO0 is connected to switch with internal pulldown enabled  
gpio.write(3,gpio.LOW)
gpio.mode(3,gpio.INPUT,gpio.PULLDOWN)  
--GPIO2 is connected to Relay
gpio.mode(4,gpio.OUTPUT)  
gpio.write(4,gpio.HIGH)  

print("Program Start")

-- Start up mqtt
m = mqtt.Client("ESP1", 120, "user", "password")
m:lwt("/lwt", "offline", 0, 0)
m:connect("192.168.15.22", 1883, 0, function(conn) print("mqtt connected")
   m:subscribe("openhab/garage/relay1",0, function(conn) print("subscribed relay1") 
   end)
end)

-- Reconnect to mqtt server if needed
m:on("offline", function(con) print ("reconnecting...")
   tmr.alarm(1, 10000, 0, function()
      m:connect("192.168.15.22", 1883, 0, function(conn) print("mqtt connected")
         m:subscribe("openhab/garage/relay1",0, function(conn) print("subscribed relay1") 
         end)
      end)
   end)
end)

 -- Switch Trigger
gpio.trig(3, "both",function (level)
   state = gpio.read(3)
   m:publish("openhab/garage/switch1",state,0,0)
   print("Sent openhab/garage/switch1 " .. state )    
end)

-- MQTT Message Processor
m:on("message", function(conn, topic, msg)   
   print("Recieved:" .. topic .. ":" .. msg)   
   if (msg=="GO") then  -- Activate Door Button
      --print("Activating Door")   
      gpio.write(4,gpio.LOW)  
      tmr.delay(1000000) -- wait 1 second
      gpio.write(4,gpio.HIGH)  
   else  
      print("Invalid - Ignoring")   
   end   
end)  

Configure OpenHAB. (These instructions assume you have a OpenHAB server already. For more info on openhab, visit https://github.com/openhab/openhab/wiki/Quick-Setup-an-openHAB-Server)

- Set up MQTT Broker if you have not done so already

- Set up the OpenHAB configuration files as follows, to display door open/closed switch status, and send door button presses.

- Configure an openhab rule to send you a tweet when the door is open or closed for testing. Send you a tweet when the door is left open for 5 minutes

Sitemap:

      Text item=Switch1
      Switch item=Relay1 mappings=[ON="Go!"]

Number Switch1         "Door Status [MAP(switch.map):%d]"    <garagedoor>       (Sensors) {mqtt="<[mqttbroker:openhab/garage/switch1:state:default]", autoupdate="false"}
Switch Relay1 "Garage Door"           <garagedoor>    (All) {mqtt=">[mqttbroker:openhab/garage/relay1:command:ON:GO]", autoupdate="false"}

transform/switch.map:

0=open
1=closed

rules

var Timer timer = null

rule "Tweet Switch Status"
when
     Item Switch1 changed
then
     var SimpleDateFormat df = new SimpleDateFormat( "YYYY-MM-dd HH:mm:ss" )
     var String Timestamp = df.format( new Date() )
     if(Switch1.state == 0) {
        sendDirectMessage('yourtwittername', 'Switch Open ' + Timestamp)
        timer = createTimer(now.plusSeconds(300)) [|   // start timer and watch for 5 minute timeout
        sendDirectMessage('yourtwittername', 'Door open too long!')
        ]
     } else if(Switch1.state == 1) {
        sendDirectMessage('yourtwittername', 'Switch Closed ' + Timestamp)
        if(timer!=null) {  // cancel timer, door is closed
            timer.cancel
            timer = null
        }
     }
end

Connect it up to the garage. The relay will connect to your garage door opener exactly the same way the push button on the wall does. You should see the two wires without too much trouble. I just connected to the wireless controller that was plugged in the wall -

Connect the other two wires from the controller to a magnetic switch that is set up to close when the garage door is closed.