I never want to push a given change

I have been using git for a little while and one thing that I would like to
be able to do is never push a given change, or set of changes.

So lets say I clone a .git repository. Then I make a couple of changes
that I don't want anyone else to see, do a commit. Then I make some
other changes that I want everyone else to see and do another commit.

How do I push just the second commit?
And how do I make it so that every other time I do a push after this that
first commit will never be sent?

Thanks,
Nathan

ps. I am really enjoying using git. Thanks.