Accent Circonflexe

ç => s

Rule: before a "a" "o" or "u", the "c" is pronounced like a "k". The 'cédille' is used to transform it into an "s", like when it is followed by "e" or "i" (putting a cedilla in those situations would be redundant and unnecessary, so it isn't done).

Example: français

é => 'et' in French, 'ay' in English, or 'e' in Spanish

Rule: the 'accent aigu' is only used on the "e". Pretty simple!

Example: cliché

à or ù (as in 'où') => a or u

Rule: This 'accent grave' doesn't sound any different, it's just meant to help differentiate written words (e.g. 'la' & 'là').

è => 'est' in French or 'eh' in English

Rule: This 'accent grave' is a bit harder to pronounce. 

Example: derrière, célèbre, pièce

ê => è

Rule: This 'accent circonflexe' is like the 'accent grave' above (pronounced like 'est' in French or 'eh' in English).

Example: crêpe, être, prêt, tête

â => 'ah' in English

Example: château, grâce, pâté

î or û => i or u

Rule: This 'accent circonflexe' doesn't sound any different. Again, it's to differentiate written words (e.g. 'sur' & 'sûr'). There is one exception (e.g. 'jeûne' is pronounced differently from 'jeune' – the former means to fast – but who cares?)

ô => 'au' in French or 'oh' in English

Example: hôtel

ë or ï  or 

Rule: The 'tréma' tells you to pronounce the second vowel independently from the first, as two different syllables. 

Example: Noël, naïve