remix-* release (npm release, github release)

For a specifix module (lib/core/debug/ide/solidity/tests)
In a new branch, bump the version in package.json, push it and create PR.
Wait for tests completion.
merge PR
build the branch ( npm run build for remix-ide ).
execute npm publish.
create new tag ( e.g git tag v0.6.1-alpha.2 ).
push the tag ( git push --tag ).
execute gren changelog --generate -t <new tag>..<previous tag> --data-source=prs.
in changelog.md remove the closed and non merged PR.
publish a release in github using the changelog.

remix.ethereum.org update

This is not strictly speaking a release. Updating the remix site is done through the Travis build:

In remix-ide repository
Switch to the branch remix_live
Rebase the branch against master
Force push
https://travis-ci.org/ethereum/remix-ide
Click More options
Click Trigger build
Select remix_live
Click Trigger custom build
Once the build is finished (can take a while) and successful, check remix.ethereum.org is updated accordingly

This is not strictly speaking a release. Updating the remix-alpha site is done through the Travis build:

https://travis-ci.org/ethereum/remix-ide
Click More options
Click Trigger build
Select Master
Click Trigger custom build
Once the build is finished (can take a while) and successful, check remix-alpha.ethereum.org is updated accordingly