If you mean the feature where you hold Alt and press digits on the numeric keypad, and when you release Alt the character with the corresponding number¹ is inserted, this isn't working for you because it's a feature of the IBM PC that Windows copied and that the Linux console copied but which the Linux GUI doesn't offer.
Under unix systems, the usual method for entering a character that isn't on your keyboard is a Compose key. Rather than memorize numbers, you press Compose and then 2 (sometimes more) characters on your keyboard. For example, Compose ' e enters
é, Compose < < enters
I don't know if Linux Mint has a Compose key enabled by default. Unfortunately, PC keyboards lack a key labeled “Compose”, so there is no standard as to which key to choose; the “Windows/Menu” key (which isn't always convenient on a laptop) or the Caps Lock key are common choices. Pull up the keyboard layout settings and make sure you have a Compose key set up.
If you need to enter a Unicode character by its number, in many applications, you can press Ctrl+Shift+U and then enter a hexadecimal number.
When it comes to rarely-used characters, where you wouldn't memorize the number anyway, there are more convenient ways to insert those characters than looking up the number and typing it. You can use a character map application such as Gucharmap to locate a character and copy it to the clipboard. You can look up the character on Wikipedia and copy it. You can draw the character on Shapecatcher and copy it.
This page describes these possibilities on Ubuntu. I think Linux Mint is fairly similar.
¹ ASCII only goes up to 127 so this is rarely used for ASCII codes.