I agree with Einer and Richard's answers, but there's one point they miss. Interspecies communications systems would work much the way the internet works today across international and especially interlingual borders. Hard work and transfer of technology.

1. As Einer points out, you'd design your output to be as easy to understand as possible, and program heuristics to understand the other species' (hopefully) simplified output.
2. As Richard says, in the extremely common circumstance where that barely works, it's a starting point. Engineers and linguists on both sides of the divide roll up their sleeves and get to work.
3. Each new species' distinct technological and infological innovations would spread across the interconnected interspecies community. Also known as: "Hey, look at how they solved this technical / data issue. That's pretty nifty, let's learn how to do that. Hey species X, check out what we learned from species Y. It's better than the way you taught us, let's use that."

I agree with Einer and Richard's answers, but there's one point they miss. Interspecies communications systems would work much the way the internet works today across international and especially interlingual borders. Hard work and transfer of technology.

1. As Einer points out, you'd design your output to be as easy to understand as possible, and program heuristics to understand the other species' (hopefully) simplified output.
2. As Richard says, in the extremely common circumstance where that barely works, it's a starting point. Engineers and linguists on both sides of the divide roll up their sleeves and get to work.
3. Each new species' distinct technological and infological innovations would spread across the interconnected interspecies community. Also known as: "Hey, look at how they solved this technical / data issue. That's pretty nifty, let's learn how to do that. Hey species X, check out what we learned from species Y. It's better than the way you taught us, let's use that."

Edit

There is an inherent feedback loop, where knowledge gained from 2. and 3. helps one improve your output and heuristics in step 1., and of course step 2 would get easier with every addition to that knowledge base.