Are there any denominations that teach their members how to hear God's voice better, as exemplified by the Apostles in Scripture? From time to time I have come across people who claim to have heard the voice of God speak to them in various circumstances. To someone who has never experienced this firsthand, this may sound a bit crazy, but the Bible is not without examples where this phenomenon is reported to have happened to the apostles. For example:
2 Corinthians 12:7-10 (ESV):

7 So to keep me from becoming conceited because of the surpassing greatness of the revelations, a thorn was given me in the flesh, a messenger of Satan to harass me, to keep me from becoming conceited. 8 Three times I pleaded with the Lord about this, that it should leave me. 9 But he said to me, “My grace is sufficient for you, for my power is made perfect in weakness.” Therefore I will boast all the more gladly of my weaknesses, so that the power of Christ may rest upon me. 10 For the sake of Christ, then, I am content with weaknesses, insults, hardships, persecutions, and calamities. For when I am weak, then I am strong.

Acts 10:9-21 (ESV):

9 The next day, as they were on their journey and approaching the city, Peter went up on the housetop about the sixth hour to pray. 10 And he became hungry and wanted something to eat, but while they were preparing it, he fell into a trance 11 and saw the heavens opened and something like a great sheet descending, being let down by its four corners upon the earth. 12 In it were all kinds of animals and reptiles and birds of the air. 13 And there came a voice to him: “Rise, Peter; kill and eat.” 14 But Peter said, “By no means, Lord; for I have never eaten anything that is common or unclean.” 15 And the voice came to him again a second time, “What God has made clean, do not call common.” 16 This happened three times, and the thing was taken up at once to heaven.
17 Now while Peter was inwardly perplexed as to what the vision that he had seen might mean, behold, the men who were sent by Cornelius, having made inquiry for Simon's house, stood at the gate 18 and called out to ask whether Simon who was called Peter was lodging there. 19 And while Peter was pondering the vision, the Spirit said to him, “Behold, three men are looking for you. 20 Rise and go down and accompany them without hesitation, for I have sent them.” 21 And Peter went down to the men and said, “I am the one you are looking for. What is the reason for your coming?”

If the apostles experienced this, it is not far-fetched to think that Christians nowadays may also experience this. In light of this realization, I'd like to know (1) if there are any denominations that actually believe in this possibility (that God still speaks to people today), and if so, (2) if there are denominations that provide explicit teaching or training to their members on how to become more sensitive to God's voice to be able to hear Him better on a more consistent basis.
Yes, this is a principle of great importance to The Church of Jesus Christ of Latter-day Saints.
Recent Teachings
In an April 2020 global conference, church president Russell M Nelson gave a discourse entitled Hear Him, including the following remarks:

We also hear Him more clearly as we refine our ability to recognize
the whisperings of the Holy Ghost. It has never been more imperative
to know how the Spirit speaks to you than right now. In the Godhead,
the Holy Ghost is the messenger. He will bring thoughts to your mind
which the Father and Son want you to receive. He is the Comforter. He
will bring a feeling of peace to your heart. He testifies of truth and
will confirm what is true as you hear and read the word of the Lord.
I renew my plea for you to do whatever it takes to increase your
spiritual capacity to receive personal revelation. (see here)

Two years prior he also gave an address discussing how &amp; why to come to recognize revelation from God. See Revelation for the Church, Revelation for Our Lives
The April 2020 sermon led to a hashtag among Latter-day Saints #HearHim (referring to hearing God) that has prompted many responses in which people have described what they do to hear Him. My own #HearHim comments are here.
Passages from canonized scripture
One of the Book of Mormon passages most commonly cited by missionaries of The Church of Jesus Christ of Latter-day Saints is Moroni 10:4-5, which specifically calls upon people to seek confirmation from God regarding the book:

4 And when ye shall receive these things, I would exhort you that ye
would ask God, the Eternal Father, in the name of Christ, if these
things are not true; and if ye shall ask with a sincere heart, with
real intent, having faith in Christ, he will manifest the truth of
it unto you, by the power of the Holy Ghost.'
5 And by the power of the Holy Ghost ye may know the truth of all
things.

One of the passages used to describe what revelation from God feels like is Doctrine &amp; Covenants 11:12-13:

12 And now, verily, verily, I say unto thee, put your trust in that
Spirit which leadeth to do good—yea, to do justly, to walk
humbly, to judge righteously; and this is my Spirit.
13 Verily, verily, I say unto you, I will impart unto you of my
Spirit, which shall enlighten your mind, which shall fill your soul
with joy;

Conclusion
Members of the Church of Jesus Christ of Latter-day Saints believe that God speaks today as He did in the past, and the church actively teaches its members to seek revelation from God for the areas of responsibility He has given them.