Here’s my analysis of Liddell, Scott and Jones’ Greek Lexicon (unabridged) entry on the word. I’ll follow it with some comments on spelling.
The basic meaning is indeed ‘throw across.’ From this usage it also came to be a verb for saying ‘to put x through y’. But more often it was used without any direct object, in which case the ‘throwing across’ or ‘putting through’ actions applied to the speaker him/herself, and the verb would mean ‘to cross over’ [=‘I throw myself over’, though the Greek uses active and not middle forms here].
When used to mean ‘throw across’ with a direct object, the verb can take on the sense of ‘throwing something in the path of something else’. So you could use it to say ‘I threw Bob into Peter’s way’ which to an ancient Greek would mean ‘I put Bob and Peter in conflict with one another.’ In addition, setting x in conflict with y can be understood as an attempt to undermine y, so the verb also can mean ‘to discredit’.
When the verb is used to mean ‘discredit someone’, it is often carries the implication that it is the person’s character that is being discredited. The usage covers a variety of discrediting – attacking someone’s character, pointing out a fault without antipathy, or blaming someone for their faults.
Finally, the verb can mean ‘to divert’. This meaning seems to me to derive from a more literal usage of the ‘put x in the way of y’ meaning. I’d contend that it is from a more metaphorical use of its meaning ‘to divert’ that the verb takes on the sense ‘to mislead’ [=to divert someone’s mind with untruth]. The verb’s senses of ‘to mislead’ and ‘to put x in the way of y’ conflate so the verb can also be used ‘to speak evasively in order to put off something.’ In the same way, the usage to mean ‘to mislead’ conflates with ‘to discredit character’ to mean 'to discredit character falsely [=to slander]. Big LSJ doesn’t put it this way, but that is my take on it.
So to sum up the words range of meaning: to throw across, to cross, to get x in y’s way, to discredit, to discredit character, to divert, to mislead, to slander.
As an aside, this is the word you’d want to use if you ever needed to translate ‘double cross’ or ‘get up in someone’s grill’ into ancient Greek. It wouldn’t mean those things by itself, but you would use it in conjunction with other words to convey those English concepts.
Spelling depends on what form of the verb you use. If you don’t want to say something specific, such as ‘I cross’ or, as a command, ‘Cross!’ or other things, the most neutral form to go with is the infinitive, ‘to cross’.
The infinitive form is diaballein. In the Greek alphabet, that would be spelled with the following letters:
delta iota alpha beta alpha lambda lambda epsilon iota nu
The standard way to do this would be all lower case letters, in which case you have to have an acute accent over the second alpha.
You could also spell it in all capital letters, which would give it the flavor of an ancient Greek inscription on stone. In that case the acute accent would be left out.
As far as font goes, I’d recommend the italicized Greek font used by Oxford University Press because I think it looks the best. But there are a variety of fonts to choose from!