Hard to improve on the great advice Grant and Brandie have provided but I thought I'd add some thoughts based on my experience getting my firm's databases under source control:

This can be a bit of work to get set-up - all the engineers will need to develop some muscle memory for it to be successful - but it's well worth the effort.

As Grant mentioned all environments should be represented by branches in the repo. My firm ended up customizing GitFlow to match our specific environment set-up. You may want to check that out to see if it would work with you.

Best practice would be for the developers to always be working in feature branches on local dbs. When a feature passes unit tests, it gets merged into (and deployed to) Dev for integration and smoke tests, then maybe Test for QA, etc.

Hope you pardon the shameless plug, but we're using the Red-gate tools to facilitate this; they've been great!