Using Alt + Keycode for accents?

Solution 1:

First hold Ctrl+Shift, then tap U and let go. An underlined "u" will appear, to which you can append a combination of characters. Hit enter after that and the new character will appear.

For instance, if I hold Ctrl+Shift and hit U, type e+9, then hit enter, an é appears. If I hit e+8 instead, an è does instead.

You can find the correct combinations using the Character Map program in Accessories. The first "0" or two that you find on certain entries can be dropped (e.g. a ç is listed as 00E7, but you only need to type the e7).

It's a bit odd coming from using the Alt method in Windows, but you'll acclimate quickly.

N.B.: If you need to frequently type many types of accented characters see Adam Byrtek's answer below for a nice method that, while it requires some setting up, can save a lot of time in the long run.

Solution 2:

Configure the compose key, press it to enter the compose mode and type e' to get "é". The mappings are very intuitive, so you don't have to learn them by heart. For example, it's easy to infer that in order to get "ü" you should type u" in the compose mode.