I'd like to suggest you three links where you can check the conjugations for Russian verbs (I suppose most people here already know these links)
http://cooljugator.com/ru/ (you can search using any form of the verb)
http://en.bab.la/conjugation/russian/ (you can search only by the infinitive form, but you can use the link below to know what is the infinitive form for a given verb)
http://starling.rinet.ru/morph.htm (Use neither capital letters nor the letter "ё" in this site, use "е" instead)
Edit: Cooljugator now declines Russian nouns and adjectives:
It seems like уметь implies or actually means "being able to (having the skill to, see Shady_arc's comment below)", while знать is more about theory. Einstein might have known (знать) how to make an atomic bomb, but it was Robert Oppenheimer who actually knew how (уметь) to make an atomic bomb.
Shady_arc adds below the verb мочь, which means "to be able to; can; may" in the sense of having the opportunity to do something, i.e., both knowing the theory and the practice of doing something, but perhaps (in the negative) not being distracted by something else - not being able to sign your name because you don't have a pen or pencil with you.
At least, that's my barely educated take on these verbs.
"Может" is third person singular, and it is rarely used for skills. "Ты можешь писать?" asks if it is possible for you to be writing, like, right now (or maybe you are too busy and have neither a pen nor a piece of paper).
Even then, it would not be a really common thing to say because usually you need a person to write down something specific—which guides what you are likely to ask.
For skills, use the verb "уметь", both in literal and metahporical sense:
- (literal) Я умею готовить яичницу. = I can make fried eggs. (I know how to do it!)
- (figurative) Ты не умеешь жить. = You do not know how to live. (you lack the "skill" of doing what a normal person is supposed to do with their life)
It depends on the stress. Note that their conjugations work differently. The verb писа́ть "write" has a consonant mutation in all present tense forms (e.g. "я пишу"). Пи́сать "piss" is a 100 % regular verb like читать.
|пи́сать "piss"||писа́ть "write"|
|past||пи́сал, пи́сала etc.||писа́л, писа́ла etc.|
|imperative||пи́сай, пи́сайте||пиши́, пиши́те|