How can access to start up menu on Macbook Air 2011?
You need to start using Internet Recovery, and once it's started (which can take a while) you can then select the menu item to install the OS. See the (rather detailed) description of the Internet Recovery system here.

Please note that with a slow internet connection, this is going to be a slow process. This is because after downloading and running the Recovery system, it is then going to go away and download the OS installer - and that is quite large.

An alternative might be to go to an Apple Store and borrow their (rather fast!) WiFi connection to do this, if you have one close by.