The answer to this is speculative because the culture itself is speculative. By speculative I mean that we don't really know the contours of the culture, since PIE is a reconstructed language. We actually have very little evidence of the language itself, let alone of the culture which utilized it. We cannot even know if there was a single culture or if the language came together due to an even older fusion.

Onto the question. From the start, you cannot really attempt to hypothesize more than the bare minimum about the deities. You would start by identifying the deities which appear common to most of the successor cultures. Ouranous/Varun for instance. Dyaus Pitr is another. Then there are deities which are unique to one branch, but not seen in another. Mitr for instance is Indo Iranian but not seen in the west (The Roman Mithras was a specific later borrowing from Persia so doesn't really count here)

You can vaguely estimate their divine functions. Ouranous/Varun appears to have been some sort of sky/universe deity with the cultures imagining the wider sky/universe as having oceanic connotations (this is partly relying on the Vedic implications of Varuna as both universe and water deity). Similarly Dyaus Pitr can vaguely be identified as some sort of sky father deity. You could also probably, based on this, posit an earth mother deity. Agni or Fire being a divinity or atleast having divine connotations is also viable.

Beyond this however you're stuck. You cannot explore any connections or hypothesize about rituals or specific characteristics because you don't really have any direct evidence. All the above conclusions come from correlating the common elements from successor cultures. This method has limits however and they come fairly quickly when you have no direct evidence.

In regards to the forum, I realise this answer contains a lot of references to speculation, but the area itself is speculative. There is little to no certainty in the subject.

A good place to start if you're interested in the subject would be the book "the horse the wheel and language" by David Anthony.