ESP8266 ESP-12 Connection I am connected with my ESP-12 through a programmer and all the AT functions work correctly. However I do not get a connection when connecting to the ESP8266 module.

I have done the following:

Set the mode both: AT+CWMODE=3

Connect to an Access Point: AT+CWJAP="&lt;name&gt;","&lt;password&gt;" (Responds with WIFI Connected and WIFI Got IP)

Set the Access Point: AT+CWSAP = "&lt;other_name&gt;","&lt;password&gt;",&lt;channel&gt;,&lt;password_security&gt;

So at this time it should be connected to my local network and I can connect to it through wifi on my laptop. However when I connect to it, it says 'Connected, No Internet' (The network the esp8266 module is connected to, has internet).

When I troubleshoot problems it says DNS is not responding.

Does anyone have a clue what to do next? Or what I might do wrong?
You can make the ESP8266 behave as a router, see Google for details.  By default it won't do this.  

You need to create two separate WIFI networks and then tell the ESP to 'route' traffic between them.  

Your ESP needs to form one network (STA mode?).  Your laptop needs to be on one network with the ESP.  The laptop needs to be configured to use the ESP as the gateway and unless your ESP has a DHCP server the laptop needs a static address.

Your ESP also needs to be a client to you router's network, and needs to take an address from the Router's DHCP server.