When I look up "to spell" in Spanish, several sites says "escribir". But if someone says "No sé escribir", how do you know if this means:
vs.
Someone could be a good speller but a poor writer, or vice versa -- how would you know which meaning was intended?
The proper translation for English "to spell" is deletrear. This verb comes from letra, and means both "to write a word letter by letter" and "to read a word aloud letter by letter". But deletrear is normally not thought of as a skill; it mostly appears in commands (i.e. when asking people with difficult-sounding names to spell them). If you are not a good speller (that is, your orthography is faulty and you make mistakes when writing words), you can say:
No sé escribir bien. = "I don't know how to write well."
Note that for skills you use saber, no poder (so it's not as in English). No puedo escribir suggests that you are physically unable to write or that you're barred from writing (e.g. you don't have time to sit down and write, or you are forbidden to write).
There's no way to mark the difference between the meanings of escribir as "to spell, to apply orthographic rules" and "to write, to compose a text". This must be resolved by context. If you are asked to write a speech or a piece of news and you don't trust yourself for this task, you can say:
No soy buen escritor.
but if you say
No sé escribir bien.
that will also work, since the meaning should be obvious (unless you're in a place with a high rate of illiteracy, which is fortunately less and less likely these days).
Bear in mind that, contrary to what happens in English, correct spelling is not a burdensome task in Spanish. Sure, there are ample opportunities for orthographic mistakes, but our orthography is fairly straightforward, so maybe that's why we don't place that much emphasis on a specific verb for spelling outside the limited usage range of deletrear. (That's also why there are no spelling contests in Spanish-speaking countries.)
"No puedo escribir" just by itself could mean that the person never really learned to read and write. Sadly, in some Latin American countries there are a substantial number of people in this situation -- especially in the senior citizen age range. Or it could be that the person has a physical impediment the prevents them from writing. More generally, that phrase by itself probably means "I'm not good at getting my thoughts down on paper."
Here are some natural ways to talk about poor spelling:
There are several ways the verb escribir can be used, and there are subtle ways to tell apart what meaning is being used. Of course you can discern the meaning by context, but here are some examples:
No se me da bien escribir.
As is the sentence can be somewhat ambiguous. Its meaning depends on the previous sentence. Maybe someone has encouraged you to write a book given the nice stories you come up with, but you think your writing skills are not good enough. Or maybe someone has just pointed out your bad orthography. In both situations you could have said that. Nonetheless, if you just don't know the spelling of a word I would use the verb in pronominal form, see the following example:
—¡Ha entrado en erupción el Eyjafjallajökull en Islandia, ve preparando un artículo para el periódico!
—¿El eyafiaqué? ¿Eso cómo se escribe?
As others have said, deletrear is a less-used verb. In the previous example you could have also said ¿Eso cómo se deletrea? but it sounds a bit akward to me (though it's perfectly valid). You also have the option to add a direct object:
—¿Eyafiaqué? ¡Soy incapaz de escribir eso!
There can be other situations where you don't use the pronominal form:
Me llamo Emma, escrito con dos emes.
But this is equivalent to:
Me llamo Emma, [mi nombre] se escribe con dos emes.
So when you have a doubt in the spelling of a word just use escribirse:
Oye, ¿"hervíboro" cómo se escribe? ¿La primera con uve y la segunda con be?
In short:
