Database/page search button for collection of links

Hi!

for my wordpress website I’d like to have a searchable link library. Something that looks & works like the one used on http://www.archiefzoeker.nl

On my WP website I’d like to have something just like the one as just mentioned above.
I wonder if it’s possible in some way to show on a single page only the search button.
After entering a search query and hit the search button, I’d like to show up all the search results matching the search query. But when you haven’t insert a search query, you won’t see any of these links.

I don’t know if you understand what i’m looking for, but if you want to have a better picutre of what i mean, just have a look at http://www.archiefzoeker.nl and search for example for ‘facebook’ or ‘social media’. I hope that will make it a little bit more clear.

Is there anyone who can help me out?

Thanks!

jLiz

PS. I don’t know if this information is necessary for helping me out, but I host my own WP website on a local host with my own domain. I hope you can help me?

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