I'm staying at the Lavilla Guesthouse in Copenhagen. It's about a 30 minute walk (13 minute subway ride) to the airport.
Btw how much is this Oresundstag? I can catch it from the airport right?
I'm not gonna go to much in depth on this whole ticket thing, since I'm no expert.
Let's just start like this.
You'll probably already know how to get from the hotel to the airport, since..well you've must have taken that trip when arriving in the first place.
At the airport you'll find an DSB ticket office right next to the pathway that'll lead you down to the train tracks.
Ask them for the cheapest ticket to and from Malmö.
You'll probably end up with some sort of 24h ticket.
DSB is the danish version of our Skånetrafiken.
Basically it's still two different operators though, which means they might have different forms of discounts for this trip.
Remember that the 105 SEK that's stated here is Skånetrafiken standard single fare price.
You can and will find cheaper prices than that.
If you get the return fare ticket (24 hour) or something even better, there's other benefits to it.
Your train ticket will also be valid on the buses in Malmö.
And well, it'll be valid on the buses and metro in Copenhagen too.
Though it's a bit trickier in Copenhagen since the city itself is divided into different ticket zones.
And well, the airport and your hotel are in two different zones.
Like I said, going too much in depth makes it complicated for me.
Ask the real experts (ticket office) about the cheapest and simplest way to reach both your destinations.
One thing I can tell you though, if you find out how to use the ticket machines in any train station, Copenhagen Airport is probably not the best possible place for you.
I beleive you'll also have to change metro train if you're heading for the airport.
DR Byen Station is the closest metro station to your hotel I think.
This metro train runs straight to Ørestad station, and guess what other train stops in Ørestad?
That's right, the train for Malmö...
This is when I'll post my old google map thingy again with all the trains.
Now updated with the Metro stations too.
http://goo.gl/maps/cQxOI