My oldest son has output difficulties. Walking together while he does most of the talking has helped him enormously.
Most of the time, I enjoy listening to my son. If you can similarly find someone in your life who enjoys listening to you and doesn't mind acting as a sounding board, just having the time to practice can really help you hone this skill.
Taking classes is not enough. It comes down to practice, practice and practice.
Also, keep a diary, it forces you to summarise your thoughts.
1. Grab a random topic, record yourself explaining it. Listen back to the recording. Try to notice anything that you don't like, for me this is awkward pauses, saying some words repeatedly such as "right" or "uhm" and in general not having a fluid and coherent flow of thoughts and phrasing.
2. Take a particular situational goal: i.e. convincing someone to do something, making a joke, acting out a scene in a film. Record yourself acting out the situation. Listen back and see if you were able to convince yourself, or you laughed at the joke or you could hear the emotion from the film scene. For me the craziest of these is telling a joke. Its amazing how much difference super slight pauses or minute changes in intonation can make. It can completely make or break a joke.
3. Teach classes or do presentations at meetups / group events. If you can record yourself and listen back to it afterwards. See if you can keep your own interest. Try to fix things you find annoying with yourself.
4. Find other people you find really impressive. For English, I think Ben Shapiro is one of the clearest, fast pace speakers on the planet. I also like the precision with which Sam Harris speaks, so I listen to these two a good bit and try to take the best from their speaking styles and incorporate it. The key is to actively listen to what they're saying and how they are saying it, trying to figure out the techniques.
In terms of measurement, be sure to save your recordings. Then you can listen to yourself at the end of every quarter or half-year and see if you can notice improvements. Also actually measure how many times you've put yourself in situations such as giving presentations, speeches, etc. That's another way to at least quantify your experience and whether or not you are giving yourself a chance to improve.
I routinely listen to Sam Harris, his explanations are amazingly clear and concise. It's quite impressive.