The murderers of street dogs usually realize their acts are illegal and incur public indignation. They avoid publicity so a curious observer has to play detective a little. Consider well whether you like to get into a detective story in a country where the only law working reliably is the law of power.
After Ukrainian way of treating stray dogs on the eve of european football championship Euro-2012 became public in Europe, municipal authorities of hosting cities learned this lesson in a specific way. And namely, they rescheduled dogs extermination activities to provide as little evidence as possible. Moreover, they restricted access to facilities such as municipal "shelters", "quarantine grounds" or burial pits. Few individuals can penetrate now, in any case not a foreigner. PETA investigators enlisted the support of Asia Serpinska and local animal protectors who accompanied them while shooting the film. KSPA doesn't recommend such trespass attempts to anyone unprepared because it can be both illegal and dangerous.
Since most public attention targets the championship host cities, smaller municipalities are usually not affected by the paranoia and continue killing openly. You "just" need to know what town, what day and time, and what place the animals will be killed next. If you realized now for the first time how difficult it is... well, it's that difficult indeed. Receiving "post factum" e-mails with photos and videos from the volunteers all around Ukraine is one story, trying to foresee one specific event is another. You need some luck and the means to react quickly (consider having a car).
The lynching of street dogs by aggressive individuals is continuously gaining in scope. Generally the same considerations apply as for towns. Please prepare yourself to hang on animal protection forum(s) and break away once local volunteers report a new case. In Kyiv, dozens of street dogs die of poison every night in a city 840 km² large. The chance you spontaneously see a poisoned dog is therefore quite low. Especially if you stay in a hotel in the downtown where street cleaners are diligent.