I have a Windows 10 Mobile phone. Can anyone tell me how to install apps from sources other than Microsoft Store?
Adding to Omar's answer:
You'll need the "Sideload apps" or "Developer mode" setting, of course. Developer mode gives you more abilities but also puts your phone at greater risk of security issues and may consume more of its resources.
Once you have those, you have to get the apps onto the phone. For either setting, you can copy the .xap/.appx/.appxbundle file onto the phone (via microSD, USB storage, MTP over USB from Windows Explorer or something, Bluetooth, etc.) or download them to the phone (from the web browser, email, OneDrive, or some other app). Then just tap (open) the files using the built-in file browser (or a third-party one).
For developer mode (and possibly also sideloading mode), you can try using the app deployment tool from the phone SDK (it's built for WP8 but I think works with W10M). For developer mode (and only developer mode), you can try enabling the developer mode portal on the phone, which starts a web server running a web app that, among other things, lets you upload app files to install (don't forget to enable authentication for the web server!).