I know there are busses but the Eurail map and information also says there are infrequent trains

There are currently no trains from Poland to Lithuania.

There are currently no trains from Lithuania to Latvia.

There are trains from Latvia to Estonia (change at Varga).

Timetables are on the operators’ own websites.

Also see Seat61.

Fares are such that it's often not worth to use a travel day for.

Back when I was Interrailing in the Baltic, I had to do a lot by bus. 
I used the Lux Express Busses, they serve a lot of destinations in the Baltic.

You can check their destinations here: https://luxexpress.eu/en/all-routes/

This is a possible route:
Warsaw - Vilnius (Bus)
Vilnius - Riga (Bus)
Riga - Varga - Tallinn (Train)

Yes, I´ve done-years ago, when one still needed a VISA to enter-now its all Schengen common area and all use the € as money. At THAT time it was the trusted old-fashioned style of the Russky poiezd=trains, going overnight from WAW and even still between these capitals. But that is long, long ago and things have changed-nicely compressed by rian above here. PLUS note that you have to spend half a day at a tiny village with nothing else to do=Valga, former border post when using the train. See also seat61.com for advice pro-train.

Right now I sit in HELsinki, where one lands on a ferry from Tallinn (very nice town to see), and FInland has thousands of Estonian workers now.

It is a fairly nice destination for if you´ve done a lot of EURope already, not at all spectaculair, it was very cheap, that is also no more since € came, so IMHO more like  a 2nd/ 3d best after others. And yes-forget that railpass, go by bus. HANSA and Lux-expr were noted as best-but the difference is not that big to worry much

IF you still want to use that pass; in Lietuva=Lithuania, you MUST first go to counter and get a free normal looking ticket by showing pass-otherwise their conductors get too much confused. There have also been reports here from people in EE where their mobile pass-and EE proclaims itself rightly as being most advanced in turning everything into mobile paperless-could not be read and they still were forced to buy ticket.

Thanks for replies. I guess we will fly Krakow to Vilnius and use busses to get to Tallinn. I confirmed with train service here in Poland there is no train to Lithuania. Wish that Eurail would update their statement that there is a train from Bialystok and their maps showing train routes through the Baltic countries. 

Hi Robert, what do you mean with the map? There imago is already showing that there’s no connection between Latvia and Lithuania. 

Oh, and if you’ve plenty time… I can suggest Klaipeda, at the coast. There’s a nice beach as well. There are trains there, from Vilnius.