Tickets used to come out somewhere between November and January, although for the last couple of years they have been much closer to the contest. It could well be that the efficient Swedes will put them up earlier though, and either way, there'll be plenty of chat on here about it so I'm sure you're unlikely to miss it.
Final tickets are like gold dust and sell out instantly, and if you are lucky enough to have the opportunity to buy one, you'd better have some organs ready to sell off.
Semi-final tickets are slightly easier to come by and slightly (but not much) cheaper, and the Monday, Wednesday and Friday night dress rehearsals tend to be more readily available and are pretty much identical to the live broadcast shows. There'll be plenty going on in Malmo and an abundance of places to watch any live shows you don't get tickets for.
They also do "family shows" on Tuesday, Thursday and Saturday afternoons, which are cheapest (but were still pretty pricey at least last year), but I'd treat those as a last resort as the acts tend to be saving themselves for the big shows that night and there isn't as much of a buzz. Not to be sniffed at if you can't get anything else and want the live Eurovision experience though!