1. Click on the menu button on the panel, and go to the tab Settings. Next, click on the Add/Remove Software app.
2. Click on the three-dot button (menu), and select Preferences. Enter the password (if necessary).
3. Next, we need to enable AUR (Arch User Repository), and enable check for updates.
4. Now we can use the search to find and install Telegram (there is a search button ).
There you can find a lot of other apps like Yandex Browser, Wine, Virtual Box, Skype and so on. There is also a console version of Telegram, which you can install using for search telegram-cli-git. Full documentation here.