Demonstrative adjectives (this, that, these, those) are words used in place of articles to indicate a specific noun. In French, they must agree in gender and number with the noun they modify:
Ce is the masculine singular demonstrative adjective:
   Ce prof parle trop. - This (That) teacher talks too much.
   J'aime ce livre. - I like this (that) book.

Ce becomes cet in front of a masculine noun that begins with a vowel or mute h :
   Cet homme est sympa. - This (That) man is nice.
   Je connais cet endroit. - I know this (that) place.

Cette is feminine singular:
   Cette idée est intéressante. - This (That) idea is interesting.
   Je veux parler à cette fille. - I want to talk to this (that) girl.

Ces is plural:
   Ces livres sont stupides. - These (Those) books are stupid.
   Je cherche ces femmes. - I'm looking for these (those) women.

Notes:
Ces is the only plural demonstrative adjective: "cettes" does not exist.
The singular demonstrative adjectives ce, cet, and cette can all mean "this" or "that." Your listener can usually tell by the context which you mean, but if you want to stress one or the other, you can use the suffixes -ci (here) and -là (there):
   Ce prof-ci parle trop. - This teacher talks too much.
   Ce prof-là est sympa. - That teacher is nice.
   Cet étudiant-ci comprend. - This student understands.
   Cette fille-là est perdue. - That girl is lost.

Likewise, ces can mean "these" or "those," and again you can use the suffixes to be more explicit:
   Je veux regarder ces livres-là. - I want to look at those books.
   Je préfère ces pommes-ci. - I prefer these apples.
   Ces fleurs-ci sont plus jolies que ces fleurs-là. - These flowers are prettier than those flowers.
The demonstrative adjective ce does not contract - in front of a vowel it changes to cet. So c' in the expression c'est is not a demonstrative adjective: it is an indefinite demonstrative pronoun.

Bon Courage!