It’s not more details that are needed here; merely relevant ones. An awful lot of the quotes, to date, deal with what Jehovah’s Witnesses [JWs] say about demonism in the 1st century A.D., and how Jesus and the apostles cast out demons, but your question does not ask about any of that. Three-quarters, or more, of the quotes already given could be omitted without the slightest impact on the few remaining relevant bits.
You ask about the JW view of the matter TODAY, and there is a dearth of information on that in current JW literature because most of it deals with 1st century situations, but fortunately I have in front of me two JW books which have relevant information. First is the 2005 book “What Does the Bible Really Teach”, and I have the 2014 edition. Chapter 10 runs from pages 96 to 105 and is headed, ‘Spirit Creatures – How They Affect Us’.
It is essential to understand at the outset that this book is produced for people interested in the JWs to study, in their homes, with JWs. It follows the question-and-answer format; a question is printed for each paragraph, and the interested student is expected to answer, going by what the paragraphs state. Once the conducting JW is satisfied that the student has grasped the JW answer given, they move on to the next paragraph/chapter. This means that all the information in this particular chapter on how demons affect people today is addressed to a person who is NOT a baptised JW.
The chapter starts by assuring the non-JW-baptised person that demons are invisibly active today but that angels will help them ‘deal with’ malign spirit influences. It gives two O.T. examples of this. It then warns that demons use Spiritism to mislead people today, especially via enquiring about the dead, but that “thousands of people who once lived in daily dread of such wicked spirits have been able to break free” (p. 103 para 13). Immediately, it says that resisting wicked spirits requires destroying books on magic, or other items that may have some demonic connection:
“People who want to serve Jehovah need to get rid of everything
related to spiritism. “That includes books, magazines, movies,
posters, and music recordings that encourage the practice of spiritism
and make it seem appealing and exciting. Included too are amulets or
other items worn for protection against evil.” (p. 103 para. 14)
Then it exhorts the interested person to strengthen their faith by studying the Bible, and praying. Of course, the exhortation is based on the goal of studying with JWs in order to be baptised as one. The chapter ends with the statement, “If you do God’s will and oppose the Devil, Satan will flee from you.-James 4:7,8” but the book is designed to convince the interested person that it is God’s will that they become a baptised JW – see all of chapter 18. That will best protect them from demons.
The Appendix has a section on identifying the religious element of ‘Babylon the Great’ – spiritistic practices being highlighted for this ‘dwelling place of demons.’ It concludes that
“Babylon the Great clearly represents the world empire of false
religion, which includes all religions that stand in opposition to
Jehovah God” [i.e. Jehovah’s Witnesses] p. 219-220
Let’s be clear here. JWs are teaching interested people that in order to avoid the ‘plagues’ God will shortly send on Babylon the Great at her destruction, they must become baptised JWs and renounce any contact they ever had with any other religion, because all religions apart from the JW one constitute spiritual Babylon the Great. That is their best chance of surviving Armageddon into a paradise earth – see chapter 18.
That was based on a JW book published 17 years earlier, the next quote from it being much more direct and telling. It comes from 'Insight on the Scriptures', Vol. 1, pp 612 to 614. The last paragraph on ‘Demon Possession’ applies Matthew 7:22-23 to modern-day demon possession exorcisms, claiming that Jesus will condemn such work done in his name, on the Day of Judgment. It switches from 1st century demon possession as detailed in the N.T. to the modern-day, and states:
“Often the wild and uncontrolled conduct of mentally unbalanced
persons is due to possession by these invisible minions of Satan.
Sometimes it is reported that spirit mediums have cast these demons
out; this calls to mind what Jesus said: “Many will say to me in that
day, ‘Lord, Lord, did we not… expel demons in your name?’ And yet then
I will confess to them, I never knew you!” (Mt. 7:22, 23)
It’s not likely that JWs will state on this forum that, Yes, they think being baptised as a JW will enable you to have angelic help to be clear of demon-possession, and that all exorcisms are done by spiritistic people who are part of Babylon the Great, but that is it, in a nutshell.
Do Jehovah's Witnesses believe in demons and that they can be cast out today? Yes, demons exist today but those claiming to cast out demons in Jesus’ name are disowned by him on the Day of Judgment, as per Mat. 7:22-23.
How do they go about casting demons out of a demon-possessed person? They don’t have any official method for that, but elders might try to encourage the 3 steps mentioned in their “Bible Teach” book, if it is a person interested in the JWs who seems to be demon possessed. The inference on p. 104, “If you do God’s will and oppose the Devil, Satan will flee from you” is that demonic harassment indicates not doing Jehovah’s will and not opposing the Devil. All baptised JWs are expected to diligently do Jehovah’s will and to oppose the Devil. Then they can expect invisible angelic help.
Do they have deliverance ministries or dedicated exorcists who specialize in spiritual warfare and related matters? No, and No.