Though this will sound very odd to English speakers, Russian has no single word that means "to spell." Russian spelling reflects pronunciation much more closely than English spelling. For the most part Russians don't need other Russians to spell a word letter by letter when they have heard an unfamiliar word.

But of course Russian spelling doesn't reflect pronunciation perfectly, so they do have ways to clarify the unclear. The most common phrase is «Как пишется это слово?» “How is this word written?” In response the other party will not name the letters of the word, but rather pronounce the word syllable by syllable, with all the unstressed vowels pronounced stressed. For instance, the word хорошо is pronounced [хəрашо], and to clarify the spelling we might have the following conversation:

Theoretically one could tell a Russian «Скажите это слово по буквам» “Tell me that word letter by letter,” but Russians will never say that to each other, and they will never tell each other how to spell a word letter by letter. (Well, maybe if they have a terrible phone connection, but never face to face. And even if the phone line is bad, they won't use the names of letters, but rather words that start with those letters.)

So for the most part Russians tell each other how a word is spelled «по слогам» “syllable by syllable.” Another phrase that nowadays means “syllable by syllable” is «по складам». That phrase actually has a bit of history. In olden days people were taught to read each letter out loud, naming the letter, and then combining each group of letters into a syllable. The names of the letters reflected the old names of the letters, not the current names. For instance, if someone wanted for some reason to spell «бабо», they would say:

буки азъ - ба, буки онъ - бо

where буки, азъ, and онъ were the old fashioned names of those letters.

For a discussion of чтение по складам see this article at gramota.ru.