ese, eso, esa and este, esta, esto
I believe "esa" and "esta" are used when referring to something feminine. Please confirm this.
How can you determine when to use "ese" or eso" and "este" and "esto"?
Just to break it down a little bit further here are some examples! @Amanda's rhyme is great for remembering this. The full form is "This and These have Ts, That and Those no."
First you have to understand there is a difference between demonstrative pronouns and adjectives. I'm not going to go over demonstrative pronouns in depth, but I will tell you they are identical in spelling** to the demonstrative adjectives listed at the bottom and translate approximately to "this one" or "that one." If you were standing in front of a row of books for sale and pointed to the one you wished to purchase you would say "Quiero ese" meaning "I want that one." In this case "ese" is being used as a stand-in, or pronoun, for the noun "book."
Esto, eso, and aquello are demonstrative pronouns in the neuter form which is a long and technical way of saying that these pronouns are stand-ins for when we refer to an unknown object, idea or abstract concept as "this" (esto) or "that" (eso). Don't be fooled, a lot of conversation revolves around things that are unknown or abstract, so we use these in many more cases than the example that follows:
Imagine you are holding a strange object in your hand and do not have any idea what it is called but would like to find out. You would ask: ¿Qué es esto? What is this? ("Esto" or "this" is a pronoun because it is taking the place of the noun, or name, of the unknown object)
Now imagine you are holding a small strange animal in your hand and would like to find out what it is called. You would ask: ¿Qué es este animal? What is this animal? (We aren't going to say ¿Qué es esto? because it is clearly an animal, not some unknown object we can't even begin to name. What we want to know is what type of animal it is. In this case we are using "este" or "this" to describe the type of animal. As you know a word that describes a noun is called an adjective, hence "this" is being used as a demonstrative adjective to describe the noun "animal")
Confused yet? Lets go back to the row of books for sale but this time when we point to the one we want to purchase we'll say "Quiero ese libro" meaning "I want that book." Because we have named the object in this example, "ese" or "this" is being used as a demonstrative adjective to describe the noun "book."
Here is a break down of the uses for your Demonstrative Adjectives:
This/These Masculine - Object close to us
este libro (this book)
estos libros (these books)
This/These Feminine - Object close to us
esta silla (this chair)
estas sillas (these chairs)
That/Those Masculine - Object a short distance away
ese libro (that book)
esos libros (those books)
That/Those Feminine - Object a short distance away
esa silla (that chair)
esas sillas (those chairs)
That/Those Over There Masculine - Object a further distance away
aquel libro (that book over there)
aquellos libros (those books over there)
That/Those Over There Feminine- Object a further distance away
aquella silla (that chair over there)
aquellas sillas (those chairs over there)
Just the tip of the iceberg but hope that helps!
**Note: The demonstrative pronouns used to have accent marks over the "e" which is how many of us learned them. Some time ago the RAE changed this rule, and they are now written without an accent in all cases except for those where disambiguation is needed. Not important for beginning learners but thought I'd put that out there.
esa = that (fem.), ese = that (masc.), esta= this (fem.), este = this(masc.). The plural forms are esas, esos(!), estas and estos. There are also some additional determiners 'aquel, aquellos, aquella, aquellas' that mean sth. like 'that one over there'. 'eso' is the neuter form of 'esa'/'ese'. (Edit: typos esto->este, eso->ese corrected)
There was a rhyme we learned in middle-school Spanish that I still find very helpful: "This and These have Ts" - So este/esta = these, ese/esa = that Wataya's answer goes into more detail about the different demonstrative pronouns, I just thought I'd share that rhyme, as it's always helped me to remember.