Swarm City Tokens (SWT) can be acquired several ways.

If you have ARC tokens you can convert them into SWT tokens by visiting the Terminal. The majority of ARC tokens minted during the crowdfund have already been converted into SWT to use within the Swarm City DApp. See the total amount of converted tokens here.

Another way to get SWT is to connect privately with a peer to exchange SWT by sending/receiving it to any public ERC-20 token address, in exchange for whatever the parties offer. Some people use https://localbitcoins.com/ to connect with other locals. Do your due dilligence, this service operates much like a craigslist site and is not regulated. 

They can be traded on a public decentralized exchange such as, ShapeShiftBittrex, ChangellyHitBTCYobitCryptoDerivatives, ChangeNow in exchange for other cryptocurrencies.