How do I Save the password to a friend's router on my LG REALM Smartphone? Each time I try to connect to this router it requires me to enter the (very long) password. 

I do not have to do that when I use my own router; I get connectivity without entering a password each time. 

What's going on?

Thanks. batpark
Or also, as rjt.rockx said,
you can use the WPS recovery tools for connect to router directly.
some apps can do that for find the WPS password :
WPS Connect - Google Play
With this feature, you can easily connect to any Router if WPS have it.(without need to entering again the password)