This is a drop in the ocean compared to what Ukraine's neighbouring countries are currently having to find ways to cope with, but as of yesterday, we've already received well over 5000 Ukrainian refugees here, a few hundred of whom want to continue through Estonia to e.g. Finland and Sweden where they have family but most of whom will stay here for now.
Over 1000 of those are children. At least in Tallinn, I gather the current plan is to not distribute the children to regular school classes for now but to open special classes next week where the children will get to keep up with basic subjects, get to learn some Estonian and get some psychological counselling, for the rest of this school year, and then, if/when it turns out they can't return home for some time yet, get assigned places in regular school classes when the next academic year starts, when they already have enough Estonian knowledge.
In other/smaller towns/counties, I think the idea is to offer the children places in Estonian schools (with some individual help) but if the families specifically want to send the kids to Russian-language schools, they'll be allowed to do so. (I guess in particular this might be a popular option among those who have come to join existing family here who have kids attending Russian schools.)
I know that for most Western countries, this all will look like very small numbers, but for us, this is unprecedented - we've usually been getting a couple of hundred asylum seekers a year, many of whom aren't actually interested in staying here but just want to get to the EU and then move on. Even with the Syrian refugee crisis in ~2015, we agreed to the EU quota assigned to us, which was 500-ish people, but ended up getting way fewer than that and 3/4 of them left within a week or two, heading for Germany or Sweden instead.
We've had a lot of Ukrainian temporary/seasonal workers over the years as well as a large local Ukrainian community so that helps a lot (having a lot of the refugees already have some familiarity with Estonia, our systems etc, or joining families/friends here who have that familiarity) but it's still the first time we've really had to deal with a crisis on this scale - accommodation needs to be found, jobs for the adults, school and kindergarten places for children, healthcare (Covid isn't over, our hospitals and GPs are struggling) - and obviously this is really just the first week. So far the public response at least has been overwhelmingly supportive; I hope this continues as the weeks go on and the number of people who've had to flee their homes and arrive here grows.