A quick search on Google gives this link.

It gives the list of verbs that use “être” in the “passé composé”.

So for instance, you will say:

Je suis monté dans la chambre
Tu es revenu
Il est devenu
Nous sommes entrés dans la maison
Vous êtes partis

you won’t say:

j’ai monté dans la chambre
t’as revenu
il a devenu
nous avons entré
vous avez parti

Beware

You can say :

j’ai monté un meuble Ikea
j’ai monté les marches du festival de Cannes
nous avons entré notre mot de passe
(and more…)

But it doesn’t have the same meaning at all

For the majority of French verbs, the past tense (passé composé*) is formed by conjugating avoir and taking the past participle:

Je parle à ma mère. —> J’ai parlé à ma mère.
Elle oublie ses clés. —-> Elle a oublié ses clés.
Ils croient que tu as raison. —-> Ils ont cru que tu avais raison.

However, for a small class of exceptional verbs, most of which have to do with motion, the passé composé is formed by conjugating être and taking the past participle:

Tu rentres chez toi. —-> Tu es rentré chez toi.
Vous descendez du train. —> Vous êtes descendus du train.

These are the "Dr. & Mrs. Vandertrampp" verbs. I do not find the mnemonic helpful, but everyone is different. (The problem is that having an exhaustive list of these verbs isn’t very useful; what you need is to know while speaking which type of verb you have.)

Devenir
Revenir

Mourir
Retourner
Sortir

Venir
Aller
Naître
Descendre
Entrer
Rentrer
Tomber
Rester
Arriver
Monter
Parvenir
Passer

In addition to this finite list of weird verbs, all reflexive (subject=object) verbs conjugate with être:

Je me demande s’il à raison. —> Je me suis demandé s’il avait raison.
Elles se parlent. —-> Elles se sont parlé.

Note zero: This is not as bad as it looks. Except for naître/mourir, all of these are verbs about "moving your body" and you get used to it. The list is also repetitive; for instance, 4 entries are just forms of venir.

Note one: The worst for English speakers is naître. This verb is weird in both English and French, but it’s weird in different ways between the languages. In English, it’s weird because the only way to express this concept is with a passive "to be born" even though 98% of the time you are not actually talking about the birthing process, and in French it’s weird because it’s an être verb and not an avoir verb. So when you hear « Je suis né à Genève, » you tend to think "I am born in Geneva….wait what?" but of course they are saying "I was born in Geneva."

Note two: Participles conjugating with être show gender/number agreement:

Il est revenu.
Elles sont revenues.

Note three: If a "VANDERTRAMP" verb takes a direct object, it conjugates with avoir.

Tu es sortie hier.
Tu as sorti le chien hier.