Boku ni mo yoku wakarimasen

Modern Ukrainian as well as Belarusian and Russian languages use the Cyrillic script as their writing system. So how can someone who is not familiar with them tell the difference just by seeing a text? It's not that difficult actually. (Please keep in mind that it's modern official languages we are talking about.)

• Ukrainian: In Ukrainian (and Rusyn) alphabet there are such unique letters: ‘є Є’, ‘ї Ї’ and ‘ґ Ґ’*.
• Belarusian: Belarusian's unique letter is ‘ў Ў’.
• Russian: Russian's unique letter is ‘ъ Ъ’**.
It means that when you meet these letters you already know the correct answer. *Sometimes you can find letter ‘ґ’ in Belarusian texts as well but not in official ones. **‘Ъ’ is not a Russian-only letter (also in Bulgarian, Rusyn and some non-Slavic scripts) but this is what makes Russian different from other two.

These tips are a bit more tricky:
• Not Russian: Ukrainian and Belarusian both share letter ‘і І’ which is not the case for standard Russian.
• Not Belarusian: Unlike in Ukrainian or Russian there is no ‘и И’ in Belarusian.
• Not Ukrainian: Belarusian and Russian languages share letters ‘ё Ё’, ‘ы Ы’ and ‘э Э’ (like Ukrainian ‘є’ but a mirrored one) and Ukrainian has none of them.

When you don't see any of the unique letters the easiest way to guess is by checking out how vowels ‘і/и/ы’ coexist in one text. ‘і’-s along with ‘и’-s mean Ukrainian. ‘і’-s and ‘ы’-s stand for Belarusian. And when you see ‘и’-s with ‘ы’-s then it's in Russian.

Examples
• (Ukr) Існує декілька ізводів (варіантів або редакцій) церковнослов'янської мови, які розвилися зі старослов'янської під впливом живих слов'янських говірок.
• (Bel) Існуе некалькі ізводаў (варыянтаў або рэдакцый) царкоўнаславянскай мовы, якія развіліся са стараславянскай пад уплывам жывых славянскіх гаворак.
• (Rus) Существует несколько изводов (вариантов или редакций) церковнославянского языка, которые развились из старославянского под влиянием живых славянских говоров.