Learn Spanish (Latin America): Necesitas escribir el mensaje correctamente.

The adjective for 'correct' is correcto. To turn an adjective into an adverb (words that often end in '-ly' in English), you first take its feminine form, correcta. Then, you add -mente to the end. That gives us correctamente (correctly).

Why is escribir not conjugated?

In Spanish, when you use a verb immediately after necesitar (to need), the second verb stays in its infinitive (dictionary) form. Since necesitas is already conjugated to match 'you', escribir stays as 'to write'.

I thought words ending in 'e' could be masculine or feminine. Why is it el mensaje?

You are right that 'e' endings can be tricky! However, there is a helpful rule here: Spanish nouns that end in the letters -aje are almost always masculine. This is why it is el mensaje (the message), just like el viaje (the trip) or el equipaje (the luggage).

Could I put correctamente before the verb, like 'You need to correctly write the message'?

It sounds unnatural in Spanish to put this kind of adverb before the verb. Adverbs ending in -mente that describe how you do something almost always go after the verb phrase they modify, which is why it sits at the end of the sentence here.