I have my own webserver on a micro Amazon instance. It seems it's dying under hackernews pressure :/
Any suggestion on something I could do? It's a wordpress blog on apache.
Out of the box, the configs which ship with Apache on e.g. Ubuntu are virtually engineered to fail if your blog ever gets a traffic spike.
Install a caching plugin for Wordpress.
Copy the output of Wordpress for that blog post to a static .html file and use mod_rewrite to point requests for the post to that file.
Turn off plugins you don't need.
Install a reverse proxy cache (such as Varnish) in front of Wordpress.
a) Throw more resources at it. I am not sure how it is done, but cloud can scale on demand from what I know.
b) If not using already, use some static page serving plugin for Wordpress, like WP Super Cache or other. This should reduce some load.