I suppose I have two or three things I want to add to this at the present time. The first is that germanictamoon is not wrong - indeed they are quite right - to point out to us that, when reconstructing sounds, we must always be aware of our limitations. We will never know with the kind of certainty I can have about the existence of the laptop in front of me (which some philosophers might want to argue is not even all that certain

) what languages we have to reconstruct really sounded like. We will never have any primary evidence, we are always forced to extrapolate and interpolate and, in the end, to make what can only ever be our best guess, based on the available evidence.
To behave like we have nothing to go on and we can't make pretty compelling conclusions is equally mistaken, however, in my view. To put it rather briefly we can look at transcriptions, we can look at how Sanskrit words were transcribed into Ancient Greek, for example. We can compare sound correspondences, we can compare similar words in different languages which all have similar meanings, e.g.:
English: father
Sanskrit: pitā
Latin: pater
We take note of the vast separation between these languages in time and location. We note the incredible similarity, despite subtle differences. We remark upon the strange fact that there is nothing intrinsic in these words that force them to mean father. Other languages do not have similar words for father, e.g. in Hebrew it is אָב ʾāḇ, in Finnish it is isä, in Nama it is ǁgûb (ǁg represents an alveolar lateral click). I'm summarising, but based on extensive correspondences, observations about how languages change from written records, as well as from what we can see in our own lifetime, knowledge of the history of these languages and their speakers, we deduce that these languages all derived from a common proto-language and that in that language was a word for father (or a word that at least had a similar meaning, such as parent, ancestor, kinsman) which gave rise to all of these "reflexes".
So how might we make deductions about what that word would have sounded like. Well we need to start by gathering as much evidence we can and look at many, many languages. Three is not enough. We need to decide, what was the original first sound, was it p, or was it f? Or was it something else? Well it's not very likely to be something else, because it turns out most reflexes start with a /p/ or an /f/ sound, in fact most of them start with /p/.
In some cases it is enough to simply take note of the majority. The reason this can be enough is that it's difficult to see why lots and lots of languages would all have changed and all in the same way. But we need to look at phonetic plausibility too. In the case of /p/ and /f/ such a change is commonly seen in the development of languages, others are less common. Historical linguistics is not a totally arbitrary, nor a fledgling field, we have a lot of information about changes which are known to have taken place, changes you can see in the written record - and in the spoken one too. We also know a little bit about phonology and we have a lot of knowledge about processes such as assimilation, dissimilation, lenition, fortition and so on and so forth.
But we don't just make comparisons between languages, we can look at changes within a language itself and, using our knowledge of the language in question, other languages, phonology and so on, we can make deductions about what changes are likely to have occurred.
We must never get carried away, we must never be too pleased with our theories, because we will never have any raw data, but there are likely possibilities, there are unlikely possibilities and there is sheer fancy.
The second thing I want to say is that, as I've said before, with Sanskrit we are not completely blind. In fact, we have, rather happily, a meticulous, written account of the production of the sounds of Sanskrit. The prātiśākhya and other śikṣā texts, as well as the schools teaching recitation allow us to talk with a fair amount more authority about Sanskrit pronunciation than, say, PIE. It is every bit as facile to wave this evidence away as it is to think that it allows us to be absolutely sure (given the enigmatic nature of the śikṣā texts and the changes we know pronunciation in the Vedic schools has undergone).
Speaking specifically about the visarga it is important to remember that it is a very late innovation of Sanskrit, deriving primarily from final -s and, secondarily, from final -r.
Which really leads me onto my third point, which is more explicitly addresses marrish's original question.
I quote Michael Meier-Brügger's "Indo-European Linguistics":
"L 309. 2) In Greek, PIE
*s is preserved when adjacent to plosives or in word-final position. Word-initially, it becomes
h- (i.e.
spiritus asper <῾->)."
We may note from his book (L 310.) the following (I shall note quote him, for he delves into a detail I dare not summarise for you here):
Compare the Greek future
héksō with Vedic
sáhate, Old High German
sigu;
The Greek
hístāmi with Latin
stāre, Vedic
sthā-trá-, Old High German
stān, Lithuanian
stóti, Old Church Slavonic
stati.