How to set up Airport Express?

What is the make & model of the wireless router that you want to extend with the AirPort Express? Is your goal to have the connection between these two routers to be wired or wireless?

Sorry, but unfortunately you will not be able to use the AirPort Express to extend the Speedtouch wireless gateway. At least not with a wireless connection between them as they are not compatible for these feature.

However, if your networking goals can support a wired connection they can both be configured for a "roaming" network which effectively does the same thing as an extended network.

The other option is to get a second AirPort Express. You then have two choices:

1. Connect the first Express to the Speedtouch by Ethernet, and then, configure the second Express to extend the first's wireless network, or
2. Configure the first Express to join the Speedtouch's wireless network. Connect the second Express to the first via an Ethernet cable. Configure the second Express to broadcast a wireless network. This would similar to a roaming network but you would not need an Ethernet connection between the Speedtouch and the first Express.

So before i go on to buy a second airpot express, I went to the service manager and asked for a new modem, the new brand is a broadtech ADSL2+8186-V2 from ELTEL group.

Will this be compatible to make the single Airport Express?

Sorry, but no. You can only extend another Apple router with AirPort Express ... so by changing to another non-Apple product you will still have the same incompatibility issue as before.