When you first install the Telegram, the app greets you with a mini slideshow explaining the benefits of the app. Yes, it's fast, free, powerful, secure and cloud-based, but you only start messaging if you can associate it to a mobile number. This is in fact the first prompt, when the app asks you to enter your country (automatically recognised) and a phone number. You simply need to confirm the country code, which is auto populated anyway and add your number — watch out for those extra zeroes if you are in the UK, for example.
The next screen immediately asks you to enter a code as a means of verification, ensuring you are the actual user of that number. Telegram will send a normal SMS with a code that you have to enter there. There is a warning that the app will call you in a minute — there's a countdown timer — and a machine will read it out. I have already installed Telegram on two devices and never got to resort to this warning call.
First steps verifying your number
The code itself is a five digit numerical sequence that you can simply copy from the notification view when the message arrives. Note how the text is delivered via SMS and not a notification from the app itself. If you don't have the notifications enabled on the Messages app or didn't have time to copy it, you will find it on the Messages app from a sender called Telegram.
If you are having issues with the SMS delivery there might be something with the number format you have used. Since the verification code will be delivered by SMS it's also worth checking your phone has network coverage and it's not only connected to a WiFi network — you could place a quick call to someone just to check. If none of these things help, there's always the option to request a verification code from a third-party app, like the desktop clients available for any platform, or a non-official app if you're using Android.
Once the code is confirmed and accepted, the next step is to enter your name and profile picture. Regardless of the name you choose, other Telegram users will see you with the name they have entered on the Contacts or Phone app, so don't worry too much about it. If you choose to upload an image as profile picture, remember this will be cropped with a circle shape — much in vogue with current design trends. If you choose to go without an avatar, the app will fill in your avatar circle with your initials and a randomly chosen background colour.