By Plane:

There are 3 possible airports fairly convenient to get to Stockholm:

• Arlanda Airport - The main airport, from here you can take the commuter train directly to Älvsjö or a Bus coach (flygbussarna.se) to the central station. There is also both normal trains and express trains going to the central station.
• Bromma Airport - The secondary airport, easiest from here would be a Bus coach (flygbussarna.se) to the central station, and then take the commuter train to Älvsjö. If you are fine with walking about 15 minutes then you can take local transport. (Easiest would be tvärbanan från Karlsbodavägen to Årstaberg and there swap to Commuter train).
• Skavsta Airport - Located in Nyköping but still marked as Stockholm according to Ryanair. Has some cheap flights. To get from here the Bus coach (flygbussarna.se) to Stockholm central station is practically the only option.

Flygbussarna:

http://flygbussarna.se/en
Cheap and reliable, 99 SEK from Bromma or Arlanda, 139 SEK from Skavsta. Will drop you off at the central train station in Stockholm.

Local transit:

All the local transit (commuter train, subway and busses) are handled by SL.
You cannot pay by Cash in the train or bus.
You can buy individual tickets with the app or buy a travel card at stations, https://sl.se/en/fares--tickets/
there is a 3 days options that could be cheaper depending on planned use.

Commuter train:

Älvsjö lies 9 minutes away from the central train station in stockholm called "Stockholm City".
All trains going southbound pass through Älvsjö (announced as "Älvsjö Stockholmsmässan").
Älvsjö Station lies about 8 minutes walk from the Venue. There is also a bus 142 going towards Telefonplan (stop: Solberga Park).
If you want to get on or off at the Arlanda station you have to pay an additional fee of 120 SEK.

Subway (T-banan):

The red line towards Fruängen stops at Telefonplan, From there you can take the Bus 142 towards Älvsjö Station (stop: Solberga Park).
This route takes about 14 minutes subway + 10 minutes bus.

Night Bus (in case of late arrival):

The bus 190 stops just outside the venue (Solberga Park) and with one swap goes to Central Bus station. http://sl.se/ficktid/vinter/H190.pdf