What is the best way to approach improving room acoustics?


I fully get I need to minimize the reflections in my video room, but it is a living room. I have many windows, multiple entrances in and out of the room, cathedral ceilings, and even a large window in a wall to view the TV from the Kitchen. 
It is the only room in the house available to do media, so please, no suggestions to just add a $100K addition to the House. 
I’m thinking of hanging heavy drapes over the windows, lots of rugs and need help with what bass traps and acoustic room treatments actually work?

I did get the Marantz 8805 with Audyssey Platinum room correction software for room tuning. It is a 7.2.4 Dolby atmos system with Rotel amps, all Focal Electra speakers and 2 Canton subwoofers.
it has the chance with help from you experts to be a special video room. The TV is the LG OLED65C8PUA.
Thanks for the recommendations.  

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Order 'Get Better Sound' by Jim Smith. DVD or Book

It will help more than we can. But you can start by covering reflective glass surfaces while critically listening to music.
Yes insulated drapes, thicker carpet and upholstered furniture willl work to deaden your very lively room.  I took these steps in our oversized family room with a large slideing glass door and two openings to hall ways and it made a huge difference.  Also going with two powered sub-woofers located apart for more even room loading is highly recommended. 
Buy the book "Premium Home Theater" by Earl Geddes.  It's a very approachable and practical book that will not only give you helpful ideas and solutions but also give you a good foundation in room acoustics in general.  Geddes writes in a way that makes it easy for even a layperson to understand the mechanics and theories behind what makes a room sound good (or bad), and I consider it a must read for anyone even remotely interested in room acoustics.  Best of luck. 
@sonyesman2 You should try Dirac Live room correct and compare with Audyssey. First place the speakers the best you can without correction given the constraints then try the correction.

PS: I do have Audyssey correction from an older Marantz currently.
The size of your room and placement of screen and main speakers - with dimensions from wall,sides and listener would be very helpful to us considering your request.