Start the container with
docker run --name truebit -ti -p 22449:80 -p 22448:22448 mrsmkl/webasm-test-docker:latest /webasm-solidity/dev.sh
Then with a web browser, go to localhost:22449. You can post a task and see if the binary search works.
If you are using Docker Toolbox and can't connect try: http://192.168.99.100:22449/
Kovan testnet:
docker run --name truebit -ti -v -v /srv/paritydata:/root/.local/share/io.parity.ethereum -p 4001:4001 -p 22449:80 -p 22448:22448 mrsmkl/webasm-test-docker:latest /webasm-solidity/kovan.sh
Rinkeby testnet:
docker run --name truebit -ti -v -v /srv/gethdata:/root/.ethereum -p 4001:4001 -p 22449:80 -p 22448:22448 mrsmkl/webasm-test-docker:latest /webasm-solidity/rinkeby.sh
On the testnets, you have to wait until the ethereum clients have synced. You also have to send them test ether to make them work.