Use option-e or ´ then e for é, and option-c for the c with cedilla (I believe it's called, like a small 5 below the c). For the apostrophes ^, ¨, and `, I can't recall, but if you have those on their own buttons (as I do, on a swedish keyboard, I don't know what apostrophes and extras you've got) you can press it first then the letter to put it on (that method works on windows too, if you use that sometime).
Thankfully, mac special characters are more easily rememberd then the windows equivalents (c-cedilla would be alt-somerandomnumber on the number keypad in windows, while mac recognizes it's a variation of c, and so designates option-c to it).
These are some of them:
option-e = é
option-c = c-cedilla (can't type it on the windows machine I'm sitting at now)
option-o = oe-ligature (o and e together)
option-shift-e = É
option-shift-c = C-cedilla
option-shift-o = OE-ligature
Other than that, I can't help you other than to take a look in the character pallette (go to System options, then International, input menu (? - i think it's called that in English), then add character pallette and select "display input menu in the menu bar", and you should be to open it from the "flag" menu beside the clock.