Unfortunately, Apple tends to make this much harder than you'd like. You can't download SDKs by themselves. They come as part of specific versions of Xcode. So you have to download the right version of Xcode. Search for "10.6", and you'll see that you want Xcode 4.1.
Once you download that, you can install it (that version will go into /Developer, so it won't break your /Applications version), or you can open up the package and find the SDKs in it. If you don't know how to crack open these packages, just install it.
Once you do that, search for "MacOSX10.6.sdk". I forget exactly where it is in that particular version.
What I do at that point is copy the sdk into a /SDKs directory. That way I always have them all.
Now, you need to add it to your current version of Xcode. You can do that by making symlinks in /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs. If you like, you can use my tiny link-sdks script for that.
UPDATE: In modern versions of Xcode (7.3+) to use older SDKs edit MinimumSDKVersion
here:
/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Info.plist