Only based on my experience, I doubt that most churches teach any theology. What theology people pick up would be by their private reading, so that could go anywhere, or by osmosis in their local church.
Osmosis is not the most efficient way!
But teaching theology would sound onerous to many church stewards, moderators, teachers and congregations. It has to be made relevant. And here's how.
One of the teaching segments of the year, perhaps aligned with Lent, or a school term, or for a couple of months after Trinity would be dedicated to 'theology'. The other 'terms' if you follow the school year, might be one OT, one NT and one contemporary life, for example, with Advent taking us up to Christmas.
Here's how the theology program might work: by using the main questions other religious approaches ask of Christian faith:
It might be the most common questions asked or claims or objections made by:
Muslims
1 Is the God Yahweh of the Bible the same as the god Allah of the Qur'an?
2 How can God be 1, yet 3, simultaneously?
3 How can God have a son?
4 Where does Jesus say 'I am God' in the New Testament?
5 Who is greater, Jesus or Muhammad?
6 Was Jesus ever crucified?
7 Which is the real religion of peace? Christianity or Islam?
8 Doesn't the Qur'an claim the Bible is corrupt?
9 We have an original Qur'an, so why can't you find an original Bible?
10 Because Islam is growing faster and stronger, won't it defeat Christianity?
See these videos for answers.
Jehovah's Witnesses
See 3, 4 and 6 above.
Modern Spiritualists (the average person)
1 Aren't all religions really the same/teach the same thing?
2 Everyone is good, deep down.
3 Isn't trying to do the right thing good (enough)?
4 Isn't the Bible just a collection of myths and legends?
5 Isn't God really the universe and in us all?
Modern atheists/materialists.
1 Isn't matter, energy and space are all there is, and all there will ever be.
2 See 1-4 for Modern Spiritualists
and, of course the
7 basic questions of Christians.
1 Why do you attend church?
2 Why do you read/believe the Bible?
3 Why do you believe in God?
4 Why are you/what is a Christian?
5 Wasn't Jesus just a great teacher, like other famous religious figures?
6 How can a good God permit evil and suffering?
7 Doesn't science disprove the Bible?
(See an earlier version: the 5 basic questions.)
In answering the questions, the basic theological themes of the Bible could be explicated.
Then the Apostles creed might be worked through, units of the questions that changed church history, as a bonus political history and the church might also be examined.
Ideally, each talk ( 'sermon') would have an accompanying article for people to study and perhaps discuss in their discipling group.
All interesting!