אני רוצה להישאר בבית הערב.

אני means I.

In this sentence, it is normally included. In Modern Hebrew present tense, the verb form often does not clearly show the person the way English does. So רוצה by itself can sound like wanting / wants, and context is needed to know who the subject is. Because of that, Hebrew usually keeps אני here to make I want clear.

רוצה is the present-tense form of the verb to want.

So אני רוצה literally looks more like I am wanting, but in normal English we translate it simply as I want. This is completely standard in Hebrew.

A useful point: in the present tense, Hebrew verbs agree with gender and number, not really with person in the same way English verbs do.

In speech, yes. In ordinary unpointed writing, not always.

• A male speaker says רוֹצֶה = rotzeh
• A female speaker says רוֹצָה = rotzah

But without vowel marks, both are usually written רוצה.

So this written sentence could mean either:

• I want to stay home this evening said by a man
• I want to stay home this evening said by a woman

Because ל־ is part of the Hebrew infinitive, and it often corresponds to English to.

So:

• להישאר = to stay / to remain

After רוצה (want), Hebrew normally uses an infinitive:

• רוצה להישאר = want to stay

So there is no separate word for English to here; it is built into להישאר.

להישאר can mean to stay or to remain, depending on context.

In this sentence, because it is followed by בבית (at home / in the house), the natural meaning is to stay:

• אני רוצה להישאר בבית הערב = I want to stay home this evening

In other contexts, the same verb can mean remain:

• אני רוצה להישאר רגוע = I want to remain calm

Literally, בבית is:

• ב־ = in / at
• בית = house / home

So literally it is in the house, but very often in natural English we translate it as at home or home.

That is why this sentence is naturally understood as stay home rather than only stay in the house.

Because בבית means at home / in the house, while הביתה means homeward / to home.

Use הביתה with movement:

• אני הולך הביתה = I’m going home

But להישאר means to stay, not to go, so you use the location form:

• להישאר בבית = to stay at home

So בבית is correct here.

In Hebrew time expressions, the definite article ה־ often works differently from English.

So הערב often means:

• this evening
• tonight

not just a literal the evening.

This is similar to other common expressions:

• היום = today
• הלילה = tonight
• הבוקר = this morning

So הערב is a very normal way to say this evening / tonight.

Yes, sometimes, but the nuance changes a little.

• הערב focuses on the evening
• הלילה focuses on the night

So:

• אני רוצה להישאר בבית הערב = I want to stay home this evening
• אני רוצה להישאר בבית הלילה = I want to stay home tonight

In everyday English, both may be translated similarly depending on context, but Hebrew does keep that time difference.

Hebrew word order is fairly flexible, and אני רוצה להישאר הערב בבית is also possible.

Both are natural:

• אני רוצה להישאר בבית הערב
• אני רוצה להישאר הערב בבית

The difference is mostly about emphasis and rhythm, not basic meaning.
The version you were given sounds natural and straightforward.

A simple pronunciation guide is:

• ani rotzeh lehisha'er babayit ha'erev — if the speaker is male
• ani rotzah lehisha'er babayit ha'erev — if the speaker is female

One small point: in להישאר, the א creates a slight break, so it sounds like:

• le-hi-sha-er

rather than one completely smooth final syllable.