Rescuing files from dead laptop's hard drive

My old MacBook Unibody Model A1342 late 2009 laptop won't start. The cause for this is probably a water damage.

Nothing major, just few drops of water in wrong place and that's that, so I'm sure that the hard drive itself isn't damaged. I'm not going to repair the laptop, but it would be nice to have the files from the hard drive.

What are my chances to rescue the files?

I viewed the guide for replacing a hard drive from this site and I'm capable to remove it, but what I should do next to rescue the files?

For example, am I able to connect the hard drive to PC?

I also have MacBook Air, so is it possible to connect the old internal hard drive as an external to it via usb?

Thanks in advance for any help.