Why is my iPhone's internet slow?

If you see No Service, Searching or SOS on your iPhone or iPad

1. Make sure you're in an area with mobile network coverage.
2. Turn mobile data off and then back on again. Go to Settings, then tap Cellular or Mobile Data. ... 
3. If you're travelling internationally, make sure your device has been set up for data roaming.

If you see No Service, Searching or SOS on your iPhone or iPad

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

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

Check your WiFi Router / Modem for --> Recommended settings for Wi-Fi routers and access points ...

For your Internet connection.

• Over Cellular: contact your Carrier (Cellular Service Provider). The agency who issued the SIM to you
• Over WiFI: Contact your ISP (Internet Service Provider), the agency who provided the Internet Service on your Modem/Router to you

However --> Connect iPhone to the Internet - Apple Support