Download from streaming app, obviously. If you want to download from websites, you need to download on computer and then transfer to iPhone. Below are some methods to help you transfer MP3 music from computer to iPhone:
iTunes is the first and official choice, obviously.
Step 1: Import MP3 files from your computer to iTunes.
Step 2: Plug your iPhone to computer and then sync with iTunes. That’s it. But note that your iPhone data will be erase before syncing, make sure you have a backup or tick on all data to transfer on iTunes.
If iTunes is too complicated and risky for you, you may turn to a third party program.
Step 1: Download and install a third party program on your computer. Go search on Google and there are dozens of this kind of programs. Here will take iTransfer as an example.
Step 2: Plug your iPhone to computer. Normally, the program will detect your iPhone model automatically.
Step 3: Find “Music” library under “iPhone” option. Click “Add Files” and choose your MP3 files from computer. The files will transfer to your iPhone automatically. Or simply drag and drop is available.
Transfer MP3 to iPhone via cloud like Dropbox and GoogleDrive is also a good idea.
Step 1: Upload MP3 files from your computer to GoogleDrive website.
Step 2: Download and install GoogleDrive on your iPhone.
Step 3: Log in your account and then download them from where you just uploaded. You can also click them to be available offline.
Here is a tutorial for your further reference: How to Transfer MP3 Files to iPhone