Particularly for English-speakers unaccustomed to such phonetic novelties, there's a common question one asks when one first encounters the un-English phonology reconstructed for Proto-Indo-European: How on earth can anyone distinguish phonemes like *t, *d and *dh from each other? The first is called a voiceless stop, the second a voiced stop but the third a voiced aspirate stop. The last one trips a lot of people out.
However, no need to fear. Treat your tongue as a science lab. Find a quiet place away from prying ears who may think you've gone mad. Just have fun playing with voicing and aspiration as you pronounce a "d" over and over a little differently each time. After repeated practice, you should get a feel for it. Of course, it often helps if you can hear what the difference is. Take a look at this wonderful page on Hindi phonetics that gives visitors an audio recording of similar differences in that language:
This site also has some other exotic phonemes that even more advanced linguistics students may find instructive. Personally, I just get a kick out the phonetic jumbalaya!
I'm probably lucky in that I grew up speaking English and French from childhood, so this whole conundrum wasn't so difficult for me. English and French are the two official languages here in Canada, of course, and my parents tried to make me a good Canadian. Alas, they tried. As I mastered both languages through gradeschool, I began to notice the subtle differences between an English "d" and a French "d" while my peers were more busy outside, discovering the joys of cigarette smoking behind the garbage bin.
It turns out that the differences between stops in both languages have to do with "voicing onset". But I didn't need the technical term to know what I was hearing. What I instinctively began to sense was what I personally called a "light d" (in English) and a "heavy d" (in French). It turned out that my ears were on to something. I was hearing the subtle fact that French "d" is pronounced with a longer duration of voicing, something I perceived as a deeper, richer sound. My English d's certainly sounded weaker somehow because oftentimes they are only semi-voiced. As a child, you learn to mimick sounds very easily in your environment and only much later do you think about it all.
Some African languages push the voicing onset to the extreme, even beyond French, and create phonemes like nd and mb. One might say that the initial nasal sound is what naturally happens when voicing extends beyond just the 'd' itself. To the other extreme, some languages don't have any voicing at all but the stop may still sound like a 'd' to English-speakers if the stop happens to lack aspiration. For example, when a Mexican pronounces Spanish queso, it may sound like 'gay-so' to an Anglophone even though the sound is in fact an unaspirated, voiceless "k".
(If you're interested in the ugly technical details, you may find this article right up your alley. It's called Perception of VOT and First Formant Onset by Spanish and English Speakers [pdf] from the University of Michigan. It shows us how easily speakers of a new language can mispronounce and misinterpret sounds because of the influences of their native language's phonology.)
Now if you're lucky enough to speak English and another contrasting tongue with significant differences in voicing onset, then you can begin to understand how a single language like IE could have had a distinction between this "light d" and "heavy d". It's not the only one (cf. Hindi or Thai).
Hopefully this layman explanation will encourage a few more zany paleoglots out there to successfully revive a dead protolanguage for their own enjoyment.