This website does not provide medical advice, and I'm not a medical professional; I'm actually a software engineer just sharing my personal experience. Always consult with your doctor before making any changes to your diet or medication.
CGM findings
We discussed what a continuous glucose monitoring is, and what various glucose-related numbers mean. I'll tell you what I figured out for myself during a year I'm using CGM.
Spikes
The first thing you'll notice is the spikes. After looking at your graphs for a few days you will soon notice that spikes are most often caused by the sugar or carbs in your meal.
Sugar
It is very well visible when you ate raw sugar–it could be soda with sugar or high fructose syrup, or a cup of juice, or maybe some ice cream. The spike will be rapid, but then the decrease of the glucose level will be rapid as well: the body will consume the free glucose pretty fast. In my graphs it would look like this:

Slower carbs
Another possibility is when the levels rise fast, but then it takes the body some time to process the carbs. Looks like this for me:

Besides meals and drinks with sugar and carbs, there might be various other reasons for the glucose level to go up–like the "dawn phenomenon" when your body thinks you really need some glucose in your blood in the morning, but at least for me, the food was the main reason of the highs.
Bringing it down
Note: I'm not using insulin or any other medications, and (hopefully) not planning to. Everything I discuss here is just my experience. If you are on insulin, you need to be much more careful; talk to your doctor. Definitely do not believe a random person on the internet (me).
Besides slowly consuming all the glucose, what brings its level down? You will soon notice that any physical activity consumes the blood glucose really fast. My favorite one is walking. It takes me 15 minutes to walk a mile, 30-40 minutes for 2 miles; 2 miles of walking decreases the blood glucose levels rapidly, like this:

I don't like treadmills at all, I prefer just walking outside, but, of course, treadmills work perfectly fine too: you don't need to run; walking with your normal pace is enough.
One other thing that I personally like, and which brings the glucose down immediately, is a hot tub, but, of course, not everyone likes hot tubs, and it's not universally good for everyone's health, so you do you, but I just noticed how it worked for me.
Base level
You will notice that if you don't have any meals containing sugar or carbs for some time, your glucose level will stabilize around some base level. When I started my CGM journey, my base level was somewhere around 180 mg/dL, which is pretty high, corresponds to A1C of about 7.9%, and got me stamped with a "type 2 diabetes" diagnosis really quick.

This base level drove me nuts because I just did not understand why would the body not consume all those extra glucose, and keep it on that high level. Even after dropping the level by exercising, walking, or just not eating for a while, it would inevitably climb up to where it was before.
Apparently, what I needed was time. Reducing the carbs to some very low amount and walking more made my base level decrease pretty well, slowly but surely. Now, after a year or so, it dropped to somewhere around 115 mg/dL, which is about 5.5-5.6% A1C, and both my endocrinologist and I think it's a pretty good achievement:

So, some good news: I found that my case is pretty manageable without medications, and I also found that it's actually pretty easy to change the diet and get rid of spikes. Let me share my experience with the low carb diet!