دي احسن طريقة عشان تنضف الاوضة.

دي means this in Egyptian Arabic for a feminine noun. It is used here because طريقة (way/method) is feminine.
If the noun were masculine, you would usually use ده instead.

In Arabic, the verb to be is usually left out in the present tense. So دي احسن طريقة literally looks like this best way, but it means this is the best way.
This is completely normal in both Egyptian Arabic and Standard Arabic.

طريقة is a feminine noun, and one big clue is that it ends in ة (taa marbuuTa). Many Arabic nouns ending this way are feminine.
That is why the sentence uses the feminine demonstrative دي with it.

It can mean better or best depending on the context. In this sentence, it means best: the best way.
In Egyptian Arabic, أحسن is very common in everyday speech. A more formal/Standard Arabic word you may also see is أفضل.

Here عشان means so that, in order to, or simply to. So عشان تنضف الاوضة means to clean the room / in order to clean the room.
In other contexts, عشان can also mean because. The exact meaning depends on the sentence.

In Egyptian Arabic, بـ often marks the normal present/habitual tense, as in بتنضف = you clean / you are cleaning.
After a word like عشان, Arabic often uses the verb without بـ, because the meaning is more like to clean or so that you clean. That is why تنضف is natural here.

Arabic often uses a full verb form where English uses an infinitive like to clean. So عشان تنضف is literally closer to so that you clean, but in English the most natural translation is usually to clean.
So the Arabic structure and the English structure are a little different, even though the meaning is the same.

Grammatically, yes, the form can correspond to you clean in this kind of structure. But in a sentence like this, it is often understood more generally, like English to clean or for cleaning.
So it is better to focus on the whole phrase عشان تنضف الاوضة rather than translating the verb too mechanically word-for-word.

This is very common in informal Arabic writing. People often leave out things like the hamza sign, so احسن may be written instead of أحسن, and الاوضة instead of الأوضة.
You may also see other small spelling shortcuts in everyday texting and online writing. Native speakers usually understand them easily from context.

الأوضة / الاوضة means the room. The base word أوضة / اوضة is very common in Egyptian Arabic.
Yes, it is specifically colloquial Egyptian. In Modern Standard Arabic, the usual word would be الغرفة.

Yes, it sounds clearly Egyptian because of words like دي, عشان, and أوضة.
A more Standard Arabic version would be something like هذه أفضل طريقة لتنظيف الغرفة. Egyptian Arabic is more conversational and uses the forms people actually say in daily life.