It depends upon which type of operating system your mobile phone runs. For example I have a mobile phone running Android 2.2 and that can be used (with an App) to become a WiFi Access Point. The App is called WiFi Tether and is free. So my laptop (or tablet) look for the Phone and connect to it by WiFi just like any other WiFi connection. This does take a lot of power from the mobile phone battery and it's best to have the mobile phone on charge when using this method. I understand you can use an iPhone in the same way.
Amazon Fire HD 8 review: A brilliant combination of function and value – with one massive caveat