how do you push only some of your local git commits?

Short answer:

git push <latest commit SHA1 until you want commits to be pushed>

Examples:

git push origin fc47b2:master

git push origin HEAD~2:main

Long answer:

Commits are linked together as a chain with a parent/child mechanism. Thus, pushing a commit actually also pushes all parent commits to this commit that where not known to the remote. This is implicitly done when you git push the current commit: all the previous commits are also pushed because this command is equivalent to git push HEAD.

So the question might be rewritten into How to push a specific commit and this specific commit might be HEAD~2, for example.

If the commits you want to push are non-consecutive, simply re-order them with a git rebase -i before the specific push.

Assuming your commits are on the master branch and you want to push them to the remote master branch:

$ git push origin master~3:master

If you were using git-svn:

$ git svn dcommit master~3

In the case of git-svn, you could also use HEAD~3, since it is expecting a commit. In the case of straight git, you need to use the branch name because HEAD isn't evaluated properly in the refspec.

You could also take a longer approach of:

$ git checkout -b tocommit HEAD~3
$ git push origin tocommit:master

If you are making a habit of this type of work flow, you should consider doing your work in a separate branch. Then you could do something like:

$ git checkout master
$ git merge working~3
$ git push origin master:master

Note that the "origin master:master" part is probably optional for your setup.