1. The Present Progressive is the equivalent to the English "Be doing"
something. The Present Progressive has two components: A conjugation
of Estar and a present participle. Notice that the name of this tense has
two words 1-Present and 2-Progressive.
This may help you to remember this is a two-part verb tense. The first
part, Present, refers to the present tense conjugation of the verb
Estar, and the second part, Progressive, refers to the Participle. The
Present Progressive uses Estar since the Present Progressive describes
a "state" that you are in.
So a present tense form of Estar is joined with a present participle to
create this new tense. The participle is the "-ing" form of a verb; for
example "running", "talking", "playing", etc. Let's look at how to form
the participle in Spanish:
We form the participle in Spanish by dropping the -ar, -er, or -ir from the
infinitive of a verb and adding one of two endings, -ando or -iendo.
to all -Ar verbs, add -ando
1) Hablar [to talk]
2) Habl-ar = habl-
3) Habl+ando = hablando [talking]
to -Er and -Ir verbs, add -iendo
1) Comer [to eat]
2) Com-er = com-
3) Com+iendo = comiendo [eating]
1) Escribir [to write]
2) Escrib-ir = escrib-
3) Escrib+iendo = escribiendo (writing)

2. Only "Ir" Stem-changing verbs continue to stem-change in the participle with a
small difference.
They go to a single letter stem-change:
O-->UE stem-changers change from O--> U;
Both E-->IE as well as E-->I stem-changers change from E---> i.
This is a stem-change which will occur in the rest of the tenses (other than the
Present Tense.)
This is why stem-changing Ir verbs have two sets of vowels in parenthesis listed:
Dormir (ue, u)
The first UE indicates the stem-change in the present tense, and
the second vowel, U, indicates the stem-change in any other tenses
where a stem-change occurs.
Decir [to Say or Tell] diciendo
Dormir [to Sleep] durmiendo
Pedir [to Request or Ask For] pidiendo
As might be expected, there are a few irregular Present Participles.
Adding the double vowel "-iendo" to -Er and -Ir stems (which already end in a
vowel) leaves the weak unaccented "i" in the middle. It isn't able to stand up
between two strong vowels. The poodle "i" will need to be replaced with a
German Shepherd "Y" in the participle:
creyendo (the weak "i" in the
Creer [to Believe] cre+iendo = creiendo middle of vowels will change to
a "y"
Leer [to Read] leiendo leyendo (see?)
Oír [to Hear] oiendo oyendo (easy!)
Caer [to Fall] caiendo cayendo (ok, you've got it!)
We combine these participles with a form of Estar to form the Present
Progressive to describe what people are smack in the middle of doing:

3. Estoy hablando. I am talking. (Right now)
Él está comiendo. He is (in the middle of) eating.
Estamos escribiendo. We are (currently) writing.
Están estudiando. They are (at this moment) studying.
The Present Progressive has a much stronger sense of immediacy in Spanish.
In other words, the present progressive is used in Spanish to explain what is
happening at this very moment. We don't use it to explain what is going on in
general.
For example, in English we can say "This semester, I am studying Spanish and
Chemistry". But you would not use the Present Progressive in Spanish. You would
use the Present tense: Este semestre, yo estudio español y química.
When I call my friend Patty, I ask ¿Qué haces? What are you doing?
She may tell me "Voy al mall" or "Preparo la cena", etc. but if I am interrupting
her in the middle of an activity, she may use the Present Progressive:
"Estoy corrigiendo las pruebas de mi clase de español 1."
There is an emotional difference, a sense of immediacy or urgency between
¿Qué haces? [What are you doing] and
¿Qué estás haciendo? [What the heck are you doing??]
Parents know this pretty well.
Note: We do not use the Present Progressive to say that we are "going to" do
something. We use the "Ir + a + Infinitive" expression to do that.