Q: I use OSX 10.6.8 and need to update Safari - how do I do this?

If you’re using a version of Safari older than 5.1.10, run the Software Update pane of System Preferences and install any Safari or security updates which appear.

If you’re using Safari 5.1.10, you can’t.

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Safari is a part of OS X and the only way to get a more modern version  is to upgrade the OS.

What is your objection to upgrading OS X, especially since that is the only way to upgrade Safari?

If you have reason to stay in Snow Leopard (older PowerPC software), have a Mac that can't run a newer OS, or simply don't want to upgrade, then your only real choice is to use a different browser. Safari in SL is now way out of date; both from a security standpoint, and has fallen far behind web standards. Firefox is your next best choice to stay in Snow Leopard, and have a browser that is still being kept up to date for that OS.

Apple profits?

The last three versions of OS X were free.

Is there a reason you want to stay four levels down on your operating system?

You can try to install Mavericks, Yosemite o El Capitan, it's free and Safari will be update automatically.

You can't update Safari without upgrading the OS, they're linked together.

If you need an update browser you can try Google Chrome, it's fast and update very often,

so you'll solve the problem and you'll be sure from newer attacks.

It would have to be El Capitan. Mavericks and Yosemite are no longer available.

Yes, if you "buy" the OS it will be in your purchase, at the new system launch the older system is no more available anymore.

Good luck, best regards