Learn Hardcore Russian: Я боюсь выступать на большой сцене, но хочу научиться это делать. - I am afraid to perform on a big stage, but I want to learn to do it.

«Боюсь выступаю» would be ungrammatical here, because выступаю is a finite verb (I perform) and you can’t use it directly after боюсь in this meaning.

So, pattern to remember:
бояться + infinitive = to be afraid to do something.

What is the difference between «боюсь» and the infinitive «бояться»?

Бояться is the infinitive (to be afraid).
Боюсь is the 1st person singular, present tense form:

я боюсь – I am afraid
ты боишься – you are afraid (singular, informal)
он/она боится – he/she is afraid
мы боимся – we are afraid
вы боитесь – you are afraid (plural / formal)
они боятся – they are afraid

So «Я боюсь» literally means “I am afraid”.

Why does the verb end in -сь in «боюсь» and «научиться»? What does that mean?

The -сь / -ся ending marks a reflexive verb in Russian.

бояться (боюсь) – to be afraid
научиться – to learn (acquire a skill)

Historically, -ся / -сь is related to “oneself”, but in modern Russian it often just marks:

Reflexive meaning:
- мыться – to wash oneself
Intransitive or passive-like meaning:
- открывать – to open (something)
- открываться – to open (by itself), to be opened
Special lexical meanings, like here:
- бояться – to be afraid
- научиться – to learn how (to do something)

So you mostly just learn reflexive verbs as separate vocabulary items; the -ся/-сь is part of the verb form.

Why do we say «на большой сцене» and not «в большой сцене»?

Both на and в can correspond to English “on / in / at”, but they’re used with different types of locations.

For events, communication, performances, surfaces, Russian often uses на:

на сцене – on (the) stage
на концерте – at a concert
на лекции – at a lecture
на стадионе – at the stadium / on the stadium grounds
на работе – at work

Saying «в сцене» would sound wrong in this meaning.
So «на большой сцене» = on a big stage / on a large stage.

Why is it «большой сцене» and not something like «большая сцена» or «большая сцене»?

The phrase «на большой сцене» uses the prepositional case, because the preposition на (in the sense of “on / at a place”) requires the prepositional.

Singular feminine noun сцена declines like this:

Nominative: большая сцена – a big stage (subject)
Prepositional: о большой сцене / на большой сцене – about a big stage / on a big stage

So:

большая сцена – nominative, used as the subject:
- Большая сцена пустая. – The big stage is empty.
большой сцене – prepositional, after на or о:
- Я стою на большой сцене. – I am standing on a big stage.

The adjective must agree in case, gender, and number with the noun, so:

на (чём?) сцене → prepositional feminine singular: на большой сцене.

Why is there a comma before «но» in Russian? Is it always required?

In this sentence:

Я боюсь выступать на большой сцене, но хочу научиться это делать.

there is a comma before но because it joins two clauses:

Я боюсь выступать на большой сцене – main clause 1
(я) хочу научиться это делать – main clause 2 (the second я is omitted but understood)

In Russian, when но (but) connects two independent clauses, you must put a comma before it.

So:

Он устал, но продолжал работать. – He was tired, but he kept working.

If но only links words inside one clause, sometimes no comma is needed:

Она не глупая, но очень умная. – comma (two predicates)
Я купил не чай, а кофе. – different conjunction, but shows the idea of no extra clause.

For two full clauses like in your sentence, comma before «но» is obligatory.

Why is it «хочу научиться» (two verbs in a row)? How does that work?

This is a very common pattern in Russian: a modal / mental verb + infinitive.

хотеть + infinitive – to want to do something
- Я хочу отдыхать. – I want to rest.
- Я хочу научиться. – I want to learn.

Here научиться itself is an infinitive: to learn (how). So:

Я хочу научиться это делать.
literally: I want to learn to do this.

You can chain verbs like this:

Я хочу начать заниматься спортом. – I want to start doing sports.
Они хотят попробовать приготовить это. – They want to try to cook this.

So “хочу + (another infinitive)” is completely normal.

Why is it «научиться это делать» and not «научиться этому» or «научиться делать это»? Are they all possible?

All three are grammatically possible, but they have slightly different nuances.

научиться это делать
- Very close to English “learn to do this / learn to do it”.
- это is the object of “делать”, not “научиться”.
- Focus can feel slightly stronger on “this” as a chunked task.
научиться делать это
- Same meaning, different word order.
- Russian often puts это earlier, but both are okay:
  - научиться это делать (a bit more common in speech)
  - научиться делать это (a bit more neutral).
научиться этому
- Literally: “to learn this (thing)”.
- этому is dative, the usual case after научиться when you name the skill as a noun:
  - научиться русскому языку – to learn the Russian language
  - научиться игре на гитаре – to learn (the) guitar

So:

научиться этому – learn this (skill / subject)
научиться это делать / научиться делать это – learn to do this (action)

In your sentence, “learn to do it” is exactly what’s meant, so the version with делать fits very well.

Why is «это» in the neuter form here? What is it referring to?

Это is the neuter singular demonstrative pronoun, often translated as “this / it”.

In «хочу научиться это делать», это refers back to the whole idea of:

выступать на большой сцене

So you can think of it as:

I’m afraid to perform on a big stage, but I want to learn to do it.

Russian uses это to refer to a situation or action just mentioned, similar to English “this / it” in such contexts.

It doesn’t change form here because as a direct object of делать, the neuter это stays invariable (same form in nominative and accusative).

Could I say «но Я хочу научиться это делать» with «Я» in the second part, or is it wrong to omit it?

You can say:

Я боюсь выступать на большой сцене, но я хочу научиться это делать.

This is grammatically correct.

However, Russian often omits repeated subjects when the subject is the same in both clauses and is clear from context. That’s why the more natural version is:

Я боюсь выступать на большой сцене, но хочу научиться это делать.

Both mean the same thing; the version without the second «я» just sounds a bit more fluent and typical in Russian.

Why is it «выступать» and not «выступить»? What’s the difference?

Выступать and выступить are an aspect pair:

выступать – imperfective: focuses on the process / repeated action
выступить – perfective: focuses on the single, completed event

In your sentence:

Я боюсь выступать на большой сцене…

the fear is about the general activity of performing on a big stage (in general, as a skill), not about one specific performance. For that general meaning, Russian uses the imperfective infinitive:

Я боюсь летать. – I’m afraid of flying (in general).
Я боюсь выступать. – I’m afraid of performing (in general).

If you used выступить, it would sound more like fear of a particular upcoming performance:

Я боюсь выступить завтра. – I’m afraid to perform tomorrow (specific event).

Could I say «Я боюсь выступать перед большой сценой» instead of «на большой сцене»?

No, that would be incorrect in this context.

на сцене – on the stage (as a performer)
перед сценой – in front of the stage (in the audience area, or standing below the stage)

So:

бояться выступать на сцене – to be afraid of performing on stage
бояться стоять перед сценой – to be afraid of standing in front of the stage

Since you’re talking about performing, you need на сцене, not перед сценой.

Is there any difference between «Я боюсь выступать на большой сцене» and «Мне страшно выступать на большой сцене»?

They’re close in meaning but not identical in nuance.

Я боюсь выступать на большой сцене.
- Literally: I am afraid to perform on a big stage.
- Emphasizes your personal, inner feeling of fear.
- Neutral, straightforward.
Мне страшно выступать на большой сцене.
- Literally: It is scary to me to perform on a big stage.
- Slightly more emotional, can sound more about the experience of fear at that moment.
- Common in speech, especially about how something feels:
  - Мне страшно заходить туда. – It feels scary to go in there.

Both are correct; in your original sentence, «Я боюсь…» is the more straightforward choice for “I’m afraid of…” as a general fact.