New ios update

Check why it is not working. Without which you cannot update iOS. --> Recommended settings for Wi-Fi routers and access points ...

Connecting to Wifi is first part and then getting connected to Internet is the second

1. If you are connected to a Wifi, doesn't necessarily mean you are connected to internet. If you are not connected to wifi could be a problem of iPhone settings or Router/Modem Settings
2. If you are not connected to internet is the sole issue of Router / Modem Settings. Contact you ISP immediately

You can update through your computer. See here: https://support.apple.com/en-us/HT204204