To save a phone number from a received or missed call to contacts, you have to just simply tap on phone number or user icon. You need to do a quick tap (not to do tap and hold). After a quick tap you should see options Add to contacts, Call, Message etc.
But even a quick tap may not work, if you did "tap and hold" before and you didn't delete anything. In this case you need to close (not hide) and reopen recent calls app.
You can close recent calls app via overview, using an overview button. If you don't have an overview button on your Android phone or you don't know how to close apps, then you can turn off and turn on the phone.