I would like to use Travis CI to build and publish distributions to Artifactory. Does anyone have an example configuration that does anything like this they could share? I'm trying to put the pieces together, but I'm new to Travis and it's hard to see what goes on behind the scenes.
You should be able to get that working with the JFrog CLI, which is made for exactly such use cases.
You will have to download and configure it as part of your travis build steps.
Install
curl -fL https://install-cli.jfrog.io | sh
Configure (assume you have the needed environment variables set)
jfrog rt config --url ${RT_URL} --user ${RT_USER} --apikey ${RT_API_KEY}
Now you just run your build and upload the results with (see docs for full details)
jfrog rt u ...