"Can you give me clean ones?"
Where is the "can" in the Hungarian sentence here? (ie: using "tud" as an auxillary verb? with the infinitive of "adni"?)
"Nekem tudsz tisztákat adni?" is not right?
(Is this a case where normally in Hungarian you would leave the "to me" as implied, rather than stating "nekem"?)
The most likely way to interpret the Hungarian sentence is that you're making a request of somebody: either "Will you give me some clean ones?" or "Can you give me some clean ones?" are good English translations of it. "Will" would probably be better, I guess. The indirect object "me" is implied.
Going back from English to Hungarian, you kind of have to realize that "Can" in the English here is just being colloquially polite; the speaker probably isn't really asking whether the other person knows how to give him some clean things. So tud would be out of place in the Hungarian sentence.
I can't think of any way to ask this question in English without using some kind of auxilliary verb that wouldn't have an equivalent in Hungarian.
Yes, I think the closest interpretation is "Will you...". And since the speaker is I, the "to me" part can be omitted. Unless the clean ones should be given to someone else. And the sense of future is carried by the simple present. So, just imagine "Will you give (me) some clean ones?" with "Will you" omitted. Maybe it is not natural to omit here but I have heard people say in everyday speech things like "Have a minute?", "Care for a drink?", "Feel like a walk?". The only difference is that the Hungarian version is normal, it is not really omitting anything that "should be there". It is a very common way of making a simple request, or asking someone to come along. "Eljössz moziba?" - Will you come to the movies with me?