I’ve installed LibreOffice in Windows 7 and have no problem writing
the " ñ " using Alt+164.
On another computer where I’ve installed LinuxMint only, I cannot write " ñ "
in OpenOffice Writer either with Alt+164 or AltGr + ^ + n.
How can I insert " ñ "?
ñ ñ You will find the ñ letter (small Latin n with tilde) in the LibreOffice insert special characters. On my system it is in the left hand column and about twelve rows down.
ALT+164 is Windows specific and is a decimal number. The Unicode Hexidecimal equivalent for 164 is actually 00F1. On a Linux Mint system you can type the character ñ directly by pressing Ctrl and Shift together then U (release) then typing 00F1(space). Sounds a little complicated at first but it is very flexible.
You do not need to type the leading zeroes for Unicode input, thus CTRL+SHIFT+u+f1.
this is great… Under Ubuntu it works, as Oweng suggested… Ctrl + Shift + letter U + letter F + number 1 (letters U, F and number 1 does not need to be pressed at the same time, but one after another).
This is great : CTRL + SHIFT together, then f, then 1, then SPACE on my system (as in @petermau’s post). I sat there looking at it for a moment while nothing happened. 
now we all know how to press ñ although, I am not going to use it in my work
Try to find that character in menu Insert → Special Character… when you find it, try to create shortcut for that symbol - some ideas how to do it can be found here LO writer: insert special characters by shortcut keys
Following a suggestion frome the OpenOffice forum ( [Solved] Special Characters (View topic) • Apache OpenOffice Community Forum ) I recently installed the ‘Compose Special Characters’ Extension from http://www.productivityapps.com/csc.html . Due to the way of implementation it should work on any system LibO / OpenO … is running on. The extension is working neatly for me. I have to admit though that I don’t need it very often.
About the Compose Special Characters extension on AskLibO: see also the link in @Ljiljan’s answer in this thread, and Part II in this answer. 
Sorry! I obviously had missed to notice some valuable information.