[ this answer can be eloborated ]
no matter what sect or section of Islam one belongs to, the criteria for dua being accepted is the same. i will try to lay a brief answer to your question, as from what i understand, acceptance of the dua is the concern.
FROM THE QURAN
You (Alone) we worship, and You (Alone) we ask for help (for each and everything) (1:5)
this verse is the foundation for making dua (note that dua is also worship).
And when My slaves ask you (O Muhammad صلى الله عليه وسلم) concerning Me, then (answer them), I am indeed near (to them by My Knowledge). I respond to the invocations of the supplicant when he calls on Me (without any mediator or intercessor). So let them obey Me and believe in Me, so that they may be led aright (1:186)
in this verse Allah ﷻ shows us the basic criteria for dua being accepted. we must acknowledge the nearness of Allah ﷻ by His infinite knowledge and we must ask from Him without any intermediaries and what we ask should be something that always brings us close to Allah ﷻ and something that pleases Allah ﷻ.
And your Lord said: "Invoke Me, [i.e. believe in My Oneness (Islamic Monotheism) and ask Me for anything] I will respond to your (invocation)" (40:60)
and this is the verse in which Allah ﷻ has commanded us to ask from Him. there is nothing any other created being can do to help us, all the power is with Allah ﷻ.
FROM THE SUNNAH
it is through our beloved prophet ﷺ that we get much clarity and further instruction on dua. how to make dua, what kind of dua to make, preferred times to make dua, preferred places to make dua, what happens when we make dua and the importance of making dua are just a few clarities we can find.
i will mention a few relevant ahadith towards acceptance of dua, in sha Allah.
Narrated Abu Huraira : Allah's Messenger (ﷺ) said, "Allah ﷻ said, 'I am to my slave as he thinks of Me (Bukhari 7505)
first and foremost what we have to understand and to believe is that, Allah ﷻ is the only one who can respond to our dua and only He can answer them. and we must have firm faith that our dua will be answered. always make dua with certainty.
there is a narration by Abu Huraira :
Make dua to Allah ﷻ when you are certain of a response (Al-Tirmidhi)
with that being understood, we must also know that there are numerous conditions for dua to be accepted and not to be accepted as well. the focus of your question was directed towards acceptance of dua but i think what's more important is to know how one's dua stands a chance of not being accepted. only when you know what nullifies something, then only you can be firm upon what you stand or believe.
namely, the conditions that dua cannot be accepted are, making dua for sin or anything Allah ﷻ has forbidden. dua for severing or cutting the ties of kinship, dua against a pious believer, making dua while you are consuming haram and being hasty.
not to be hasty when making dua (al-Bukhaari, 6340, Muslim, 2735)
not to make dua for sin and for severing ties of kinship (Muslim 2736)
consuming haram lessens/invalidates dua (Muslim 1015)
(note: even the conditions are laid out like this always remember that Allah ﷻ has all the sovereignty and He does whatever He wills, so we can only assume based on this instructions that one's dua has a lesser chance or no chance of being accepted but in reality, it is only Allah ﷻ who knows)
only knowing about how to make our dua being accepted is not enough, we must also know what happens when make dua.
Abu Sa'id al-Khudri reported: The Prophet ﷺ, said, "There is no Muslim who calls upon Allah, without sin or cutting family ties, but that Allah will give him one of three answers: He will quickly fulfill his supplication, He will store it for him in the Hereafter, or He will divert an evil from him similar to it." They said, "In that case we will ask for more." The Prophet said, "Allah has even more" (Musnad Aḥmad 11133)
"Nothing can change the Divine decree except dua"
[Musnad Ahmad, 5/677; Ibn Majah, 90; Jami Al-Tirmidhi, 139]
may Allah the mighty and sublime grant us mercy and guide us to the straight path.
Allah knows best