This might not be the right approach, but it's the one I use...

I balance it by "keeping score" and erring on the side of caution. For every story/fact about myself that I share, I prompt them to share one and vice versa. And if they get on a roll and start sharing a lot, I let them talk and actively listen.

Then, of course there are some moments (which I try to make rare) when I monopolize the conversation about me because it is something highly important to me or to the relationship. But I consider that balanced when my partner gets on a roll and starts talking "me, me, me."

I also try to only share what is appropriate for the moment...for instance, if we went to a park and saw a carousel, I might say, "My father used to take my brother and me to the carousel in the summer." and end it there...instead of, "My father used to leave my brother and me at the carousel because he couldn't deal with us after the divorce. He was so depressed and became and alcoholic. I was do angry at him for so long....etc. etc. etc.

i.e. don't bring up drama if you don't have to.

After a while, I get into the rhythm of the relationship, then I don't have to "keep score" anymore and things happen a lot more organically.

Hope that helps.
Scales

That does make since, so kind focus on the moment

I agree with taking some time to get to know a person and it does take time...'the rhythm of a relationship' is well put I think MissS

I try to get to know them as friends first, at least that's what works for me. A couple of guys had invited me on dates recently, and I like them as people, but I don't want to be in a relationship, and paradoxically, when I explain my expectations, it only seems to attract them even more. I don't like the idea of full on dating, it's too much pressure even if I wanted a relationship. I prefer to get to know the person before I get seriously involved with them. But meeting as friends takes all of that pressure off and helps me stay relaxed throughout interactions instead of trying too hard or over analysing.

I focus my attention on the person I'm talking TO, guage their reactions to what I'm saying. If I see them squirm, I've clearly divulged TMI.

This is why in-person dating is sooo much better than online dating. Are these people you're meeting in-person, online or both?