QUESTO (this, this one) - QUELLO (that, that one)
These pronouns are used as in English, with two differences:
in Italian they are gender-sensitive, according to the object they indicate;
the Italian ones can translate both this and this one.

quello that / that one (masculine)
quella that / that one (feminine)
quelli those / those ones (masculine)
quelle those / those ones (feminine)

These pronouns may be used either as a subject of the sentence, or as an object, in which case the English translation always includes ...one:

They may be used for any other case (genitive, dative, etc.).

Sometimes, when demonstrative pronouns are the subject of a nominal sentence (a sentence whose verb is to be, which describes a condition or a quality rather than a real action),
it is possible to reverse the subject of the sentence, this gives more emphasis to the pronoun.
Especially in the spoken language, questo and quello are often strengthened by the use of the following adverbs:

qui
here

qua
here

ĺ
there

là
there

Note that while in qua and qui the last vowel is not accented (although they sound as if it actually was), là and ĺ need an accented vowel.

In written language, instead, it is preferrable to avoid adding these adverbs to the pronouns.

The result is as follows:

masculine
singular

questo qui / questo qua
this one here

questi qui / questi qua
these ones here

feminine
singular

questa qui / questa qua
this one here

queste qui / queste qua
these ones here

masculine
plural

quello ĺ / quello là
that one there

quelli ĺ / quelli là
those ones there

feminine
plural

quella ĺ / quella là
that one there

quelle ĺ / quelle là
those ones there

COSTUI (that man) - COSTEI (that woman) COSTORO (those people)

These pronouns are somewhat similar in meaning to egli (he), ella (she) and essi / esse (they), but they carry a meaning of detachment from whom is speaking, as if referring to a stranger, or to somebody whom the speaker is not in relation with.
For this reason their English translation is more often that man rather than this man, but several other expressions would be correct: that fellow, the bloke, the guy, he, she, and so on, according to the context.
Instead, these pronouns would never be used to address a friend, or somebody who is well-known.
They are not too frequently used in the spoken language, while they are very common in literature.

When demonstrative pronouns questo (questa, questi, queste) and quello (quella, quelli, quelle) are followed by a noun, they turn into adjectives. In this case, a few changes occur to match phonetically the first letter of the following word.

When questo is followed by a noun beginning with a vowel, it makes an elision.
i.e. it drops the last ...o, whose place is taken by an apostrophe.

Pronoun quello instead, changes when the following name begins with a vowel it turns into quell', with an apostrophe;
when the following name begins with Z or with S + consonant (sb..., sc..., sd..., etc.) it remains as it is;
when the following name starts with a consonant it turns into quel.

questa only makes an elision (i.e. quest' with an apostrophe) if the following name begins with a vowel.
And quella changes in a similar way.
The elision may be sometimes omitted to give these demonstrative pronouns a stronger emphasis, almost as underlining the noun they refer to.
In these cases, they are spelled (and pronounced) throughoutly, to stress their meaning.

Pronouns questi, queste and quelle do not have any phonetic changes.
The adjective quelli, instead, changes into quei or into quegli.
quegli is used when the following word begins with a vowel, or with z...,
or with cluster s + consonant (sb...; sc...; etc.)
These phonetic changes take place according to the next following word, not necessarily to the noun which the adjective relates to.

These rules are summarized in the following table:
the following noun starts with...

pronoun used alone (no noun)

followed by any vowel

followed by any consonant

masculine
singular

questo

quest'

questo

feminine
singular

questa

quest'

questa

masculine
plural

questi

questi

questi

feminine
plural

queste

queste

queste

pronoun used alone (no noun)

followed by any vowel

followed by Z, or S + consonant

followed by any other consonant

masculine
plural

quello

quell'

quello

quel

feminine
plural

quella

quell'

quella

quella

masculine
plural

quelli

quegli

quegli

quei

feminine
plural

quelle

quelle

quelle

quelle